Ms. Pelosi described the deal on Friday as a “work in progress” her members could not yet support. “What isn’t in it yet is enough enforcement reassurances regarding workers, provisions that relate to workers and to the environment,” she said.

A spokesman for Mrs. Pelosi did not say on Sunday if the president’s move would accelerate her timetable or alter her negotiating strategy. “It’s disappointing but not surprising that President Trump would try to force Congress to reinstate the status quo of Nafta, instead of working constructively with Congress to improve his proposed agreement to actually protect and strengthen American workers,” said the spokesman, Henry Connelly.

There is no language in Nafta’s authorizing law that requires congressional approval for withdrawal from the treaty, although some of Mr. Trump’s staff believe the matter is ambiguous and could end up in court.

Congress, at Mrs. Pelosi’s instigation, could proactively pass legislation, with a veto-proof majority, blocking him from doing pulling out of Nafta. But most legislative leaders think that scenario is unlikely.

Mr. Trump’s announcement, which came shortly after he agreed to hold off on new tariffs against China in face-to-face negotiations with the Chinese leader Xi Jinping, was also intended to emphasize his tough stance on trade as he softens his posture with Beijing.

The move took many of Mr. Trump’s economic advisers by surprise: In the lead-up to the Argentina trip, most of them were said to believe that scrapping Nafta was off the table.

But Mr. Trump has grown increasingly frustrated with Democrats, telling people in his orbit that he believes they would rather turn their backs on a “great deal” than see him achieve one of his top campaign goals, according to a person who has spoken to the president in the past week.