Eduardo Bravo, past chairman of the Mexican Entrepreneur Association, said he was relieved by the way the issue had been resolved on Wednesday but warned that there was still a rough road ahead, describing the White House’s behavior as “very schizophrenic.”

“Really, you have to maintain hope and keep working to maintain the relationship,” he said. “There’s a lot of work to do.”

In interviews with politicians, analysts, economists, business leaders and former diplomats, a general sentiment had emerged throughout the day on Wednesday that Mr. Trump’s threat to withdraw from the treaty using an executive order was mostly a piece of political theater — aimed as much at his voting base as at Mexico and Canada — and not something to get terribly worked up about.

Some speculated that the news of the order was a controlled leak intended to gauge the reaction of the other Nafta parties and put them on the defensive.

“The generous analysis would be that he’s playing brinkmanship and trying to up the ante,” said Arturo Sarukhán, a former Mexican diplomat to the United States. “This is a way to sort of rattle the scabbard and say that he’s got a saber in it and say, ‘If you don’t agree to my demands, then I’m going to end up pressing the nuclear button.’”

Still, the news came as a surprise to many who had been watching the process closely.

After months of tough talk by Mr. Trump, his administration had appeared to be on track to begin negotiations over Nafta as soon as this summer. Administration officials circulated a draft of a letter in March that laid out goals in a negotiation, an obligatory step in the process. The letter suggested a far more modest approach than Mr. Trump had threatened, leaving much of Nafta intact.