Hours after imposing steep tariffs on Canada, President Trump raised an issue that even the American lenders whose cause he’s championing find perplexing: the access, or lack thereof, of U.S. banks to the Canadian market.

On Tuesday, Mr. Trump wrote in a post on Truth Social, “Canada doesn’t allow American Banks to do business in Canada, but their banks flood the American Market.” He added sarcastically, “Oh, that seems fair to me, doesn’t it?”

While this issue doesn’t often come up in conversations with prominent American bank executives, it appears to be increasingly on the president’s mind.

Mr. Trump mentioned the Canada banking issue early last month as part of a broader criticism against what he views as the unequal economic balance between the United States and its northern neighbor. Writing on Truth Social, Mr. Trump said Canada “doesn’t even allow U.S. Banks to open or do business.”

Here is the actual state of play for U.S. banks in Canada:

Can U.S. banks operate in Canada?

Canada’s banking sector is dominated by the “Big Six,” the half-dozen institutions including the Royal Bank of Canada and TD Bank. They are permitted to take deposits, extend mortgages and advise corporate clients — all the core activities for banks. And Canadian customers disproportionately still prefer to do their banking in person, as opposed to online, meaning it would require a major physical presence for any entrant to attempt to enter the market.

Additionally, U.S. banks are restricted in what they can do in Canada.

Foreign banks, including American ones, must either work with a Canadian middleman, establish a Canadian subsidiary or receive special government permission to do business. Unless they agree to follow Canada’s stringent banking rules that include holding a hefty sum of cash-like assets in reserve at all times, they cannot operate retail branches that take deposits under around $100,000.

Given how dominant Canada’s homegrown banks are, any international bank that tries to compete faces “an additional regulatory burden for what would begin as a small prize,” said James R. Thompson, associate professor of finance at the University of Waterloo.

The upshot is that U.S. banks have minimal operations in Canada. The largest American lender, JPMorgan Chase, says it has roughly 600 employees in Canada, out of more than 300,000 worldwide. Many international banks limit themselves to areas that don’t involve lending, such as offering investment advice to wealthy Canadians or local companies.

So Mr. Trump is incorrect in asserting that American banks cannot do any business in Canada, but it is true that they are hamstrung in their activities.

Why is Canada so restrictive?

While there are more than 4,000 banks in the United States, Canada has just a few dozen, and more than three-quarters of deposits are held by the Big Six.

For decades, Canadian political leaders have crowed about that restrictive financial regulatory model. They argue that fending off foreign entrants in the country’s mortgage market helped the country largely avoid the 2008 collapse south of its border.

In light of Mr. Trump’s criticism, Maggie Cheung, a spokeswoman for the Canadian Bankers Association, was quick to point out on Tuesday that foreign banks were an integral part of the banking landscape. She said 16 U.S. banks were operating to some degree in Canada, with a cumulative of nearly $79 billion in assets — a statistic that the nation’s prime minister, Justin Trudeau, also cited on Tuesday.

“American banks are alive and well and prospering in Canada,” Mr. Trudeau said.

But in relative terms, their successes are small. U.S. bank assets represent 1 to 2 percent of the $6.5 trillion held by banks operating in Canada writ large.

“The major impediment faced by U.S. banks,” said Laurence Booth, professor of finance at the University of Toronto, “is simply they can’t compete with the Canadian banks as they don’t have the scale, while they can’t take any of them over as there are restrictions on foreign ownership.”

Do Canadian banks ‘flood’ the U.S.?

International banks — including Canadian ones — are largely free to establish U.S. arms. The United States is a more attractive target for international banks than Canada, both because it is a hub for world finance and because its market permits more exotic, higher-profit lending activities like 30-year mortgages. (The most common mortgage in Canada carries a five-year term.)

The largest Canadian bank in America, TD Bank, operates more than 1,000 U.S. branches through a Delaware subsidiary. That size puts it in line with well-known regional lenders like Citizens and Fifth Third.

The Canadian Bankers Association said the six largest Canadian lenders held less than 3.5 percent of U.S. bank assets.

Is this even an issue for Wall Street?

Big U.S. banks had plenty of hopes that Mr. Trump would decrease regulations, encourage merger activity and slash taxes. Expanding their presence in Canada was not on the list.

A U.S. banking industry trade group, the Bank Policy Institute, said Tuesday that it had released no statements on the matter, and no bank chief executive has taken up the rallying cry.

More pressing for the global banking industry are Mr. Trump’s tariffs, which have helped push the industry’s stocks down 8 percent over the past month, according to the KBW Nasdaq Bank Index.

The sweeping tariffs on Canadian, Mexican and Chinese products that President Trump imposed on Tuesday could strain the system that collects import duties and the government agencies that enforce those fees, trade and legal experts said.

Collecting import duties is usually a routine task, but the new tariffs are being imposed on Mexican and Canadian goods, many of which have been imported into the United States duty-free for many years. Adding to the challenge is the sheer volume of goods subject to the new tariffs — U.S. imports from China, Mexico and Canada totaled over $1.3 trillion last year, or about two-fifths of all imports.

The tariffs apply a 25 percent duty on goods from Mexico and Canada and an additional 10 percent on imports from China.

Importers typically employ customs brokers to calculate and pay tariffs to the government agency that collects them, U.S. Customs and Border Protection.

Adam Lewis, a co-founder and the president of Clearit, a customs broker, said that it would not be hard to tweak software to collect the new tariffs, but that a crucial part of the tariffs payment system might need significant adjustments. Importers must buy a “customs bond,” a type of insurance that guarantees the duties will be paid. Mr. Lewis said some customers might have to increase the size of their bonds to cover the extra tariff payments.

“Many of their products were coming in duty-free, and all of a sudden there’s going to be a 25 percent increase,” he said. “It’s quite large.”

In addition, policing importers for tariff evasion will now become a much bigger task for Customs and Border Protection and the Department of Justice. Some importers may try to avoid tariffs by understating the cost of goods in customs declarations or by falsely claiming they were imported from countries not subject to tariffs.

“The greater the breadth and severity of these new tariffs, the greater the likelihood that at least some potential importers may want to misrepresent the value or the origin of their goods,” said Kirti Vaidya Reddy, a former federal prosecutor who is now a partner at the law firm Quarles.

If the government finds that an importer has not paid duties, customs officials are likely to demand that the importer pay what is owed and a penalty that can double or even triple the amount due.

In a statement, a customs agency spokeswoman said: “The dynamic nature of our mission, along with evolving threats and challenges, requires C.B.P. to remain flexible and adapt quickly while ensuring seamless operations and mission resilience. These tariffs will help maintain America’s global competitiveness and protect American industries from unfair trade practices.”

Some evasion cases have become the subject of criminal prosecutions. Last year, a Miami importer pleaded guilty to participating in an import scheme involving Chinese truck tires that the Justice Department said had cost the United States more than $1.9 million in forgone tariff revenue.

But stepping up enforcement efforts is likely to require that the Justice Department devote significantly more staff to pursuing tariff evasion cases, which, lawyers said, can take time to build.

“The Department of Justice has the personnel and infrastructure to do it, but these cases are complex, transnational and document-heavy,” said Artie McConnell, a former federal prosecutor who is a partner at the law firm BakerHostetler. “You can’t rush it, and prosecutions likely won’t come quickly.”

Minutes after President Trump’s latest tariffs took effect, the Chinese government said on Tuesday that it was imposing its own broad tariffs on food imported from the United States and would essentially halt sales to 15 American companies.

China’s Ministry of Finance put tariffs of 15 percent on imports of American chicken, wheat, corn and cotton and 10 percent tariffs on other foods, ranging from soybeans to dairy products. In addition, the Ministry of Commerce said 15 U.S. companies would no longer be allowed to buy products from China except with special permission, including Skydio, which is the largest American maker of drones and a supplier to the U.S. military and emergency services.

Lou Qinjian, a spokesman for China’s National People’s Congress, chastised the United States for violating the World Trade Organization’s free trade rules. “By imposing unilateral tariffs, the U.S. has violated W.T.O. rules and disrupted the security and stability of the global industrial and supply chains,” he said.

President Trump has contended his tariffs are essential to stopping the flow into the United States of fentanyl, a synthetic opioid that has caused hundreds of thousands of deaths through overdoses.

But the U.S. imposition of tariffs “will deal a heavy blow to counternarcotics dialogue and cooperation,” Lin Jian, a spokesman for China’s Ministry of Foreign Affairs, said at a news briefing.

Mr. Trump has now tagged almost all goods from China with an extra 20 percent in tariffs since taking office in January. He announced 10 percent tariffs on Feb. 4 and another round on Tuesday. Mr. Trump also moved ahead on 25 percent tariffs on Mexico and Canada on Tuesday, after a monthlong delay.

China had responded to the February tariffs by immediately announcing that it would start collecting, six days later, additional tariffs on liquefied natural gas, coal and farm machinery from the United States. But those tariffs combined hit only about a tenth of American exports to China, making them much narrower than Mr. Trump’s comprehensive tariffs.

China’s action on Tuesday was much broader. China is the top overseas market for American farmers, wielding considerable influence over prices and demand in the commodities markets of the Midwest.

By targeting imports of food, Beijing repeated its response to tariffs that Mr. Trump imposed during his first term. China put tariffs on American soybeans in 2018 and shifted much of its purchasing to Brazil.

But the strategy backfired then: Mr. Trump responded by placing more tariffs on Chinese goods. Because China sells much more to the United States than it buys, it quickly ran out of American goods to impose tariffs on. And American farmers had some success in finding other markets for their crops.

China’s tariffs in 2018 also had less of a political impact in the United States than Beijing’s leaders had hoped. In 2018 Senate elections in three of the top soybean-exporting states, voters gave little evidence they held the Chinese action against Mr. Trump or the Republican Party. All three states saw Democratic senators replaced with Republicans that year, as social issues proved more compelling for many voters than trade disputes.

Yet China has potential trade weapons that go beyond tariffs on food. In early February, Beijing implemented restrictions on exports to the United States of certain critical minerals, which are used in the production of some semiconductors and other technology products.

Blocking key materials from reaching the United States, a tactic known as supply chain warfare, carries considerable risks for China. Beijing is struggling to attract foreign investment. China’s leaders have also stated that attempting to bolster the country’s domestic economy, weighed down by the fallout of a devastating real estate slowdown, is a priority.

Beijing could make it even harder for American companies to do business in China, but that could also hurt foreign investment. In addition to effectively preventing 15 companies from buying Chinese goods, China’s Ministry of Commerce added another 10 American companies on Tuesday to what it calls an “unreliable entities list,” preventing them from doing any business in China.

Many of the companies that China penalized on Tuesday are military contractors. But the Ministry of Commerce also blocked imports from the biotech firm Illumina. It accused Illumina, which is based in San Diego, of violating market transaction rules and discriminating against Chinese companies.

Chinese market regulators said in early February, after Mr. Trump imposed tariffs, that they had launched an antimonopoly investigation into Google. Google has been blocked from China’s internet for more than a decade, but the move could disrupt the company’s dealings with Chinese companies.

Mr. Lou, the National People’s Congress spokesman, signaled his country’s emerging strategy in dealing with Mr. Trump’s tariffs by calling for closer trade relations with Europe.

“China and Europe can complement each other’s strengths and achieve mutual benefit in many areas of cooperation,” he said at a news conference ahead of the opening on Wednesday of the annual weeklong session of China’s legislature.

But Europe has its own trade disputes with China, notably over electric vehicles. European politicians and business leaders have voiced concern about how to cope with an expected further flood of exports this year from China, which has embarked on a far-reaching factory construction program.

China’s rapid rise since 2000 to global pre-eminence in manufacturing, with a third of the world’s output, has come to a considerable extent at the expense of the American share of global industrial production, according to United Nations data. European nations have been wary of closing factories and relying on low-cost imports from China.

Mr. Trump has moved much faster on China tariffs during his second term than he did in his first. In 2018 and 2019, he imposed tariffs of up to 25 percent, in stages, on imports worth about $300 billion a year. He then concluded a trade agreement with China in January 2020, leaving in place 25 percent tariffs on many industrial goods while cutting 15 percent tariffs on some consumer products to 7.5 percent and canceling a few other tariffs.

By contrast, Mr. Trump has now imposed 20 percent tariffs on all goods that the United States imports from China, worth about $440 billion a year. That includes some products, like smartphones, that he omitted during his first term.

Mr. Trump’s actions this year have raised average tariffs on the affected Chinese imports to 39 percent — compared with just 3 percent before he took office in 2017. Apart from China, Canada and Mexico, the United States imposes tariffs averaging about 3 percent on most trading partners.

China’s average tariffs on goods from most of the world are twice as high, and much higher on imports from the United States.

In Mr. Trump’s first term, the Chinese government reduced taxes that it charges the country’s exporters. That gave them room to cut prices and offset at least part of the tariffs for their customers, which include many small American businesses as well as big retailers like Walmart, Amazon and Home Depot.

As another way around tariffs, some Chinese exporters shifted the final assembly of their products to countries like Vietnam, Thailand or Mexico, while keeping the production of core components in China. Mr. Trump is now trying to stop some of the trade through Mexico, which critics of Chinese exports see as a backdoor into the U.S. market.

Many Chinese exporters resorted to using the so-called de minimis exception to tariffs: dividing shipments into many packages, each with a value of less than $800. Each shipment is then exempt from tariffs and customs processing fees and mostly omitted from customs inspections and American imports data.

At least $1 of every $6 worth of American imports from China is now arriving through these de minimis shipments.

In early February, Mr. Trump issued an order briefly halting the de minimis tariff exemption for goods from China, Mexico and Canada. After packages quickly accumulated at American airports, he delayed the order for shipments from China until procedures could be developed to handle them, and postponed for a month his order for de minimis imports from Canada and Mexico. On Sunday, he again delayed action on those imports from Canada and Mexico.

Wu Xinbo, dean of the Institute of International Studies at Fudan University in Shanghai, said that by retaliating now, “China sends a strong signal to the Trump administration that a unilateral tariff doesn’t work — you have to sit down to talk to us and to negotiate with us.”

Alexandra Stevenson contributed reporting from Beijing, and Chris Buckley and Amy Chang Chien from Taipei. Li You contributed research.