WASHINGTON — President Trump told the leaders of Mexico and Canada on Wednesday that he would not immediately move to terminate the North American Free Trade Agreement, only hours after an administration official said he was likely to sign an order that would begin the process of pulling the United States out of the deal.

In what the White House described as “pleasant and productive” evening phone calls with President Enrique Peña Nieto of Mexico and Prime Minister Justin Trudeau of Canada, Mr. Trump said he would quickly start the process of renegotiating Nafta — not abandon it, as he said he would do during the 2016 presidential campaign if he could not rework the deal to his satisfaction.

“It is my privilege to bring NAFTA up-to-date through renegotiation,” Mr. Trump said in a statement issued by the White House at 10:33 p.m. “I believe that the end result will make all three countries stronger and better.”

The announcement appeared to be an example of Mr. Trump’s deal-making in real time. It followed a day in which officials signaled that he was laying the groundwork to pull out of Nafta — a move intended to increase pressure on Congress to authorize new negotiations, and on Canada and Mexico to accede to American demands.