It was not clear whether the president would still sign an executive action to authorize renegotiation of Nafta, which he once called the worst trade deal ever signed by the United States. Washington must give Canada and Mexico six months’ notice before exiting the trade agreement, which came into force in 1994. Any action to that effect would start the clock.
But the prospect of the United States’ pulling out obviously alarmed the Canadian and Mexican leaders and prompted their calls to the White House.
The Mexican peso plummeted in trading after news broke at midday on Wednesday that the White House had drafted an executive order withdrawing the United States from Nafta. Mr. Trudeau called Mr. Trump twice, on Tuesday and Wednesday, to discuss the sudden rupture in the trade relationship between the United States and Canada.
On Tuesday, the Trump administration announced that it would impose a tariff on Canadian softwood lumber, in retaliation for what it said was unfair treatment of American dairy farmers.
The president has repeatedly derided Nafta, describing it last week as “very, very bad” for the country, companies and workers, and he promised during his campaign that he would remove the United States from it if he could not negotiate improvements.
The White House wants Congress to authorize those negotiations under legislation that would allow expedited approval of the reworked agreement, but talks between administration officials and congressional Republicans have moved slowly.
While some of Mr. Trump’s senior advisers, notably Stephen K. Bannon and the economist Peter Navarro, are eager to take strong steps on trade policy, another group — which includes Gary D. Cohn, the head of the National Economic Council — has argued for a more cautious approach, concerned that larger steps could cause economic disruptions.
Lately, Mr. Trump has taken the stronger line, moving to reshape America’s economic relationships with foreign nations. The Nafta order would come on the heels of the announcement of the new tariffs on Canadian lumber and reviews of whether steel and aluminum imports are undermining national security.
“Nafta’s been very, very bad for our country,” Mr. Trump said last week. “It’s been very, very bad for our companies and for our workers, and we’re going to make some very big changes, or we are going to get rid of Nafta once and for all.”
Walking away from Nafta would disrupt the economies of the United States, Canada and Mexico, and strain broader relations among the countries. Over the last two decades, their economies have become increasingly intertwined. The volume of trade has multiplied, and the manufacture of many goods, notably cars, involves multiple border crossings and factories in all three nations.
If the United States actually pulled out, experts said, trade with Canada would probably still be subject to a similar agreement between the two countries that took effect in the late 1980s and served as a model for Nafta. The Trump administration, however, could seek to withdraw from that agreement as well.
The shift in the rules governing trade with Mexico would be more significant. The two countries both take part in the World Trade Organization, but that allows much higher tariffs. Mexico, for instance, could impose a 37 percent tariff on American corn. The disruptions to manufacturing could also come at a hefty cost to consumers: Caroline Freund, a fellow at the Peterson Institute for International Economics, has estimated that the cost of a pickup truck might increase by $3,000.
Monica de Bolle, a senior fellow at the Peterson Institute, said: “It would be a very disruptive shock that would impact everybody. It would impact growth; it would impact companies and supply chains; it would impact workers; it would impact voters in Trump states. It’s just crazy to imagine that they would go that route.”
The suggestion of withdrawal, reported by Politico on Wednesday, raised anxieties in financial markets. The peso fell more than 2 percent against the dollar, and the Canadian dollar fell about 0.3 percent.
“Scrapping Nafta would be a disastrously bad idea,” Senator Ben Sasse, Republican of Nebraska, said in a statement. “Yes, there are places where our agreements could be modernized, but here’s the bottom line: Trade lowers prices for American consumers, and it expands markets for American goods. Risking trade wars is reckless, not wise.”
Both Mexican and Canadian officials have said repeatedly that they are ready to negotiate changes to the trade agreement. Written in the early 1990s, it is outdated in key respects: Its drafters, for example, did not foresee the rise of the internet.
“Canada is ready to come to the table at any time,” Alex Lawrence, a spokesman for the Canadian foreign minister, Chrystia Freeland, told Reuters on Wednesday.
In fact, the Obama administration negotiated changes to the deal as part of the Trans-Pacific Partnership, a broader agreement that would have supplanted Nafta. Mr. Trump withdrew from that agreement as one of his first official acts.
The Trump administration provided an indication of its own priorities in a letter circulated among members of Congress last month. While proposing some significant changes, such as strengthening the available penalties for breaches of the rules, it suggested that the administration was not seeking to alter the basic structure of the agreement, prompting relief both north and south of the United States.
The administration must send a final version of that letter to Congress to start another clock: a 90-day waiting period before negotiations. Starting both clocks would allow the White House to begin negotiations with Mexico and Canada while holding in hand the threat of walking away from the table.
It is not clear whom that would hurt most. Mr. Trump has repeatedly denounced trade deficits as a major contributor to what he sees as the nation’s broken economy.
But trade among the three North American nations is relatively balanced, particularly in comparison with trade between the United States and China.
The United States actually ran a trade surplus with Canada in 2015 and during the first three quarters of 2016, according to the most recent data available from the Commerce Department. American sales of goods and services to Canada exceeded purchases of goods and services from Canada, on average, by $1 billion a month.
The United States does run a monthly deficit of about $4 billion with Mexico, but even that is a small fraction of the roughly $28 billion monthly deficit with China.