President Donald Trump was prepared to end the North American Free Trade Agreement deal, which had governed trade relations for the past 23 years, with a dramatic announcement Saturday at a Pennsylvania political rally marking his 100th day in office.

As rumors spread of the possible action, Mexican President Enrique Peña Nieto called the president urging him not to pull out of the accord. “Let me think about it,” Mr. Trump said. Within a half hour a call came in from Canadian Prime Minister Justin Trudeau with a similar request....