The announcement followed US media reports that Trump was considering giving formal notice of pulling the United States out of the North American Free Trade Agreement.
In phone calls to Mexican President Enrique Pena Nieto and Canadian Prime Minister Justin Trudeau, Trump "agreed not to terminate NAFTA at this time," the White House said in a statement.
It added that "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."
Trump campaigned for president in 2016 on a platform that included renegotiating or abandoning the trade agreement, which he claimed was "the worst trade deal maybe ever signed anywhere" in a September debate with Hillary Clinton.
NAFTA was established January 1, 1994 under then-president Bill Clinton. It removes tariffs and allows a free flow of goods between the three partners.
Trump has repeatedly derided NAFTA as a "disaster" and claimed the deal resulted in millions of lost US industrial jobs, mostly to Mexico.
"It is my privilege to bring NAFTA up to date through renegotiation," Trump said, according to the White House statement. "It is an honor to deal with both President Pena Nieto and Prime Minister Trudeau, and I believe that the end result will make all three countries stronger and better."
Both conversations were "pleasant and productive," the statement said.
The US trade deficit in goods and services last year with Mexico was $62 billion, but with Canada the US had a surplus of $8 billion.
'Rumor' of US exit from NAFTA
Two White House officials told the Politico news website on Wednesday that a draft executive order for the United States to exit NAFTA was in the final stages of review, and could be unveiled within a week or two. The New York Times had quoted a senior administration official saying Trump was likely to sign such an executive order.
But late Wednesday Commerce Secretary Wilbur Ross brushed off the reports as "rumor."
"There was a rumor today that there would be an executive order, just a rumor, and my practice is to comment on things we have actually done or are doing as opposed to commenting on rumors," Ross said.
According to The Washington Post Trump is expected to tell Congress that he intends to re-negotiate the deal, but also hold the threat of exiting the agreement to gain more concessions from Mexico and Canada.
The administration's talk of exiting NAFTA has run into opposition from several prominent Republican lawmakers, including border senators John McCain of Arizona and John Cornyn of Texas, Politico reported.
"I'd be glad to have renegotiation of some of the terms of it, because a lot of time has passed," McCain told Politico. However a withdrawal would "be disgraceful and a disaster."
Trade tension with Canada
The Trump administration has slapped tariffs in recent days on some imports of Canadian timber and threatened to retaliate against Canadian moves that harm US dairy farmers. Timber and milk, however, are not covered by NAFTA.
The softwood lumber dispute between Washington and Ottawa has been ongoing for at least 35 years, with US producers accusing their Canadian counterparts of exporting lumber at subsidized prices and harming US businesses.
Lumber is an important component of the massive US construction and home-building industry. Most US homes are made with wood framing and some entirely of wood.
Earlier this week, the US Commerce Department announced it was imposing tariffs of up to 24 percent on Canadian softwood lumber.
Canada's dairy sector is protected by tariffs on imports and controls on domestic production as a way to support prices for the country's farmers.
The latest dairy trade row was triggered when Canada extended those policies to apply to ultrafiltered milk, a product used in cheese production and at the center of a thriving US export business.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)