A quick resolution would also allow negotiators to bypass complications stemming from the upcoming Mexican elections on July 1, which appear likely to usher in a left-leaning president who has sharply criticized Mr. Trump over his broadsides against Mexico. And the White House could promote a revised Nafta as a political win ahead of the congressional midterm elections in November, while giving the president’s top trade advisers room to turn their attention to resolving a potential trade war with China, which has fired back against American trade actions with punitive measures of its own.

White House trade advisers are meeting with their Mexican and Canadian counterparts in Washington this week to try to hammer out areas of consensus on the most difficult issues of the talks. Robert Lighthizer, the United States trade representative, Foreign Minister Chrystia Freeland of Canada and Economy Minister Ildefonso Guajardo of Mexico were expected to kick off trilateral talks on some of the pact’s thorniest issues over dinner in Washington on Thursday night.

Prime Minister Justin Trudeau of Canada struck an optimistic note on Thursday, saying the countries were having a “very productive moment,” a sharp change in tone from previous comments about a Nafta resolution.

“We are in a moment where we are moving forward in a significant way,,” Mr. Trudeau said. “Hopefully there will be some good news coming.”

He is expected to attend the two-day Summit of the Americas in Peru next week, alongside Mr. Trump and President Enrique Peña Nieto of Mexico.

Yet hurdles remain, including how far the United States is willing to go in surrendering many of its negotiating goals, given Mr. Trump’s frequent and vocal criticism of Nafta. Negotiating partners are still waiting to see whether the United States will compromise on the tough requests it has made over the past eight months of negotiations. Many of those demands, including those linked to American auto production, have angered business groups and lawmakers, who say such requirements would actually hurt companies and workers by shifting more manufacturing out of the United States.

A quick resolution would necessitate concessions from the Trump administration, potentially resulting in a deal not significantly different from the one Mr. Trump has denounced as a travesty and embarrassment.