Trump has already withdrawn the United States from the 12-nation Trans-Pacific Partnership agreement negotiated by his predecessor, Barack Obama, although that deal had not been ratified by Congress.
"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", a White House statement said.
"If I'm unable to make a fair deal, if I'm unable to make a fair deal for the United States, meaning a fair deal for our workers and our companies, I will terminate NAFTA", he said.
"He expressed that he was very much thinking about cancelling", said Trudeau.
And Congress has yet to approve Trump's nominee for US trade representative: Robert Lighthizer, who has advocated using existing trade law more aggressively to combat unfair trading practices.
USA farmers provided $2.5 billion in soybeans, meal and oil to Mexico past year, making it the nation's No. 2 market overall and the leading purchaser of US meal and oil.
Mexico's peso and Canada's dollar fell against the United States dollar, with the peso shedding about 1.5% in just over an hour, while Canada's "loonie" lost about 0.45%. According to an analysis by Banco BASE, it was the biggest single-day depreciation for the currency since January 18.
Several agriculture lobby groups in Washington were told USAgriculture Secretary Sonny Perdue, confirmed by the Senate on Monday, met with Trump on Wednesday evening to dissuade him from withdrawing from Nafta.
The peso recovered to 19.03 to the dollar Thursday, after the governments issued parallel statements committing to renegotiating NAFTA.
The White House made the surprise announcement in a read-out of calls between Trump, Mexican President Enrique Peña Nieto and Canadian Prime Minister Justin Trudeau.
Trudeau said the president seriously raised the possibility.
"I highlighted. a disruption like cancelling NAFTA, even if it eventually, theoretically might lead to better outcomes, would cause a lot of short and medium term pain for an bad lot of families". Below are two big things each country would like to get out of the talks.
NAFTA has a direct impact on Arizona - Mexico is Arizona's top trading partner - and, many in our state's business community have been watching closely for anything that might affect it.
Whether it's unfair Chinese trade practices, the North American Free Trade Agreement he's dubbed a "disaster" or Iran's destabilizing actions, Trump has kept up much of his bold campaign rhetoric. White House officials had earlier said the administration was considering efforts to withdraw.
"It likely reflects certain staff and structural problems in the White House, which are worsened by the ideological clash between competing factions", says Eric Shimp, a former US diplomat and adviser on trade at the law firm Alston & Bird.
"You don't go and float these rumors and have the markets crash, and currencies, and threaten bilateral relations just to prod your own party into acting in Congress", Guajardo said.
He reiterated his long-standing assertion that the 1994 trade agreement has been "very good for Canada". Instead, he said the deal will be renegotiated. "And I said, I will hold on the termination; let's see if we can make it a fair deal". "But we're going to give renegotiation a good, strong shot".
In recent days Trump also has taken a harder line with Canada, blasting a recent change in the dairy pricing policy there that mostly dealt with a cheese-making product called ultrafiltered milk.
And the Commerce Department said Monday it would begin charging a tariff on the import of softwood lumber from Canada into the United States, alleging Canada was improperly subsidizing its domestic timber firms.
Stories suddenly appeared in the Washington Post, Politico, CNN and the New York Times saying sources within the White House were seriously considering a draft executive order to cancel NAFTA. "But the well will be poisoned", he said.