Despite indications earlier Wednesday to the contrary, President Donald Trump agreed not to terminate the NAFTA treaty "at this time" in afternoon phone calls with the leaders of Mexico and Canada, the White House said.

Here's the readout from the White House:

Late this afternoon, President Donald J. Trump spoke with both President Peña Nieto of Mexico and Prime Minister Trudeau of Canada. Both conversations were pleasant and productive. President Trump agreed not to terminate NAFTA at this time and the leaders agreed to proceed swiftly, according to their required internal procedures, to enable the renegotiation of the NAFTA deal to the benefit of all three countries. President Trump said, "it is my privilege to bring NAFTA up to date through renegotiation. It is an honor to deal with both President Peña Nieto and Prime Minister Trudeau, and I believe that the end result will make all three countries stronger and better."

Both the Canadian dollar and the Mexican peso rose against the U.S. dollar after the release of the White House statement.

The Trump administration had been mulling an executive order on withdrawing from the North American Free Trade Agreement, the three-nation deal Trump repeatedly slammed on the campaign trail, Politico reported earlier, citing two White House officials.

A draft version of the order had existed, Politico and NBC News reported. Politico reported that the order was in the "final stages of review" and could have been "unveiled late this week or early next week."

Trump previously said he wanted to renegotiate NAFTA, arguing that the agreement has punished American workers and companies. The order, though, could be used as a negotiating tactic with Mexico and Canada, the other NAFTA parties.

This is a breaking news story. Check back for updates.

—CNBC's Jacob Pramuk contributed to this report