Canada has said it will not allow the United States deadline to govern the trade talks. After marathon talks this month, Mr. Lighthizer and Ms. Freeland scheduled no formal meetings in Washington this week.

“We will keep working as long as it takes to get to the right deal for Canada,” Mr. Trudeau said at a news conference in New York on Wednesday.

Asked what would happen if the United States moves forward with just Mexico, Mr. Trudeau said: “We will keep working on a broad range of alternatives. A broad range of paths are ahead of us.”

Canadian and American officials have tried to avoid negotiating in public, but in recent days their differences have started to spill out. Speaking at an event sponsored by Politico in Toronto on Wednesday, David MacNaughton, Canada’s ambassador to the United States, said Canada wanted protection from the Trump administration’s use of tariffs on national security grounds.

Upcoming elections in Quebec, a province whose economy is heavily dependent on dairy, have also complicated negotiations for Canada’s leaders as they look to close a deal with the United States.

“It seems like Canada has decided it’s too risky before the Oct. 1 Quebec elections to make any deal on Nafta, so the U.S. and Mexico deal will go forward and get signed, get stuck in the refrigerator,” said Lori Wallach, the director of Global Trade Watch at Public Citizen, a consumer advocacy group. “Canada and the U.S. will talk and at some point they will all get stirred up and served together in Congress in 2019.”

Canada is the largest export market for America, and members of Congress from both parties have been adamant that it should be included in any agreement with Mexico. Congress must ratify major trade deals, and an agreement that excludes Canada is expected be difficult to pass. There is also an ongoing legal debate as to whether the president has the authority to terminate Nafta on his own. If Nafta is terminated, Canada and Mexico could continue to trade on its terms or work together on their own new free trade agreement.