While Mexico's top negotiator, economy minister Ildefonso Guajardo reiterated Monday that the next step was for Canada to rejoin the discussions on the trilateral accord, Trump said, "We could have a separate deal or we could put it in the same deal".
The U.S. president made the announcement today in the Oval Office, with Mexican President Enrique Pena Nieto joining by speaker phone.
"We're going to call it the United States/Mexico Trade Agreement", he said.
Al Jazeera's Kimberly Halkett, reporting from Washington, DC, said Trump was "delivering" on promises made during his successful presidential campaign to renegotiate major trade deals affecting U.S. workers.
Shares of top automakers rallied Monday after the US and Mexico reached a preliminary trade deal, ending months of uncertainty for vehicle production.
"We'll have a formal news conference in the not-too-distant future", about the trade pact, Trump said to Pena Nieto.
United States stock indexes hit fresh records Monday as the U.S. and Mexico struck a tentative a bilateral trade deal that's expected to replace the 24-year old North American Free Trade Agreement.
They said nothing could come from Trump's unilateral imposition of tariffs in order to get foreign governments to negotiate seriously.
A spokesman for Canadian Foreign Minister Chrystia Freeland said the country would continue to work toward an agreement and was in regular contact with trading partners. The Mexican president said he wanted the former. He even added later in the day that he had "just signed a trade agreement with Mexico", which can not happen without the USA first nixing NAFTA. Provisions of the new agreement Monday are likely to include new requirements for automakers' infotainment systems and parts that were previously exempt from the final composition list under the old agreement.
The U.S. president also threatened America's northern neighbor with penalties if there is no agreement. Other key issues are Chapter 19 anti-dumping panels, which the USA wants to kill but which may be a deal-breaker for Canada, as well as Canada's dairy sector, which Trump is targeting.
"For some time now, (Trump) has been very prudent in referring to Mexicans, or he hasn't said offensive things", Lopez Obrador said.
Canada still needs to join the agreement, and any deal would need to be approved by Congress before it can go into effect.
The deal also would require 40 percent to 45 percent of auto content to be made by workers earning at least $16 per hour, the second official said.
"We'll see if Canada can be part of deal", he said, saying the USA might simply opt for new agreements with both its neighbors.
There is no deal reached yet with Canada, people familiar with the agreement said.
A USA industry source briefed on the talks said a deal had been reached. Asked about whether Mexico would be willing to sign a deal without Canada, a senior Administration official demurred, offering arguments for why the country might want to without saying that it would.
Canada will be joining the talks after the United States and Mexico come to an agreement to replace NAFTA, which was signed in 1994.
The president indicated his administration and Mexican officials will try to sell their Canadian counterparts on the details, but left open the door to one-on-one deals with both countries.