US President Donald Trump's trade deal with Mexico could struggle to win approval from Congress unless Canada comes on board, lawmakers from both parties said on Tuesday, saying support from Democrats would be needed to pass a purely bilateral deal.

Trump unveiled the Mexico deal on Monday and threatened to slap tariffs on Canadian-made cars if Canada did not join the revamp of the trilateral North American Free Trade Agreement (NAFTA), which the president has long criticized.

If Trump, a Republican, tries to get the Senate to vote in favor of a bilateral deal as a replacement for NAFTA, he will face an uphill struggle to win passage, lawmakers said.

Some lawmakers said only a trilateral pact would be eligible for fast-track, 51-vote Senate approval.

A bilateral deal, on the other hand, would need 60 votes and that would require some support from Democrats, who likely would be reluctant to help Trump, they said. There are now 50 Republican-held seats in the 100-member Senate.

To get fast-track Senate ratification, "the administration must also reach an agreement with Canada," said Republican Senator Pat Toomey in a statement.

"NAFTA was a tri-party agreement only made operative with legislation enacted by Congress," said Toomey, a member of the committee that oversees trade policy.

"Any change, such as NAFTA's termination, would require additional legislation from Congress. Conversion into a bilateral agreement would not qualify for ... 'fast-track' procedures and would, therefore, require 60 votes in the Senate."

A White House spokeswoman referred questions to US Trade Representative Robert Lighthizer's comments on Monday when he said the White House was ready to notify Congress by Friday of Trump's intent to sign a bilateral document, but that it was open to Canada joining the pact.

Canadian Foreign Minister Chrystia Freeland on Tuesday started her first negotiating session at Lighthizer's office in several months and told reporters: "We are encouraged by the progress that the US and Mexico have made." 

Freeland said that Mexico's concessions on autos and labor rights on Monday would pave the way for productive talks this week as all three countries race toward a Friday deadline for a deal to modernize the 24-year-old NAFTA.

Democratic Senate Leader Chuck Schumer said a bilateral deal would face "serious legal concerns," while he also questioned a lack of details on the terms of the Mexico pact.

"I'm a little worried that this one is like North Korea (DPRK). They have a nice announcement, but then we don't see the details," Schumer told reporters in a Capitol hallway.