Trump says the new pact - known in Washington as the US-Mexico-Canada Agreement (USMCA) - will help US workers, especially in the auto industry, and better safeguard intellectual property.
The issue could ultimately be decided by the USA courts.
"Revamping the new trade agreement was aimed to preserve the view of an integrated North America with the firm belief that together we are stronger and more competitive", he said in remarks translated from Spanish.
This would forsake Congress with two choices: accept the United State, Mexico, Canada or probability constituting no deal in place.
Trade experts have long suspected Trump, who has made beating up on NAFTA a central feature of his political career, might play the termination card in an effort to light a fire under the deal's critics.
She cited a lack of enforcement tools for labour standards, drug company "handouts" and a lack of sufficiently robust measures to cut pollution or combat climate change, particularly in Mexico - and her refusal to use the deal's new name hinted at precisely why Trump wants to do away with the old one.More news: For the first time since 2013, Microsoft Office icons have been redesigned
"Now that the agreement has been signed, the Senate Finance Committee will review it with a fine-tooth comb and have the opportunity to weigh in", Grassley said in a statement.
Numerous nation's largest ports have been reporting record container volume as shippers rushed to get those items into the United States or sent overseas before the higher tariffs took effect.
The ink wasn't even dry on the signatures on the USMCA trade deal before serious doubts arose about whether the deal would ever be ratified. And while there are some instances in which the president has acted unilaterally to terminate commercial treaties, far more cases have involved the participation of Congress, he said.
Hailing the deal as "modern and balanced", the president said at the signing ceremony that it has been "well-reviewed" and he doesn't expect to have much problem in Congress. "The president needs to talk to Congress on this", the Ohio Democrat told CNN on Sunday.
House Minority Leader Nancy Pelosi and Senate Minority Leader Chuck Schumer both made clear on Friday that the trade agreement will need protections for workers and the environment, along with other changes, to get their support.
Rubio's office said Monday that the senator had asked Lightizer to look into additional trade actions to protect Florida growers, and that Lighthizer had committed to requesting a fact-finding investigation and taking corrective action.