"We'll get rid of the name NAFTA, has a bad connotation because the United States was hurt very badly by NAFTA for many years, and now it's a really good deal for both countries, and we look very much forward to it", he said.
U.S. and Mexican negotiators have been working for weeks to iron out differences in order to revise the almost 25-year old North American Free Trade Agreement, while Canada was waiting to rejoin the negotiations.
Mexican President Enrique Peña Nieto was on speakerphone and says he hopes NAFTA partner Canada will eventually be incorporated into the deal.
Both the United States president and the Mexican president, Enrique Peña Nieto, said they had an understanding and thanked each other during a phone call listened into by reporters. Canada is part of NAFTA, but it was not included in the U.S. -Mexico agreement announced Monday.
And there are political reasons to keep Canada inside the regional bloc: "Mexico will have a hard time selling "Trump's deal" back home if Canada does not think it is a good deal", said Daniel Ujczo, a trade attorney with Dickinson Wright PLLC.
The Trump administration wants a higher percentage of auto production to come from within the NAFTA bloc before qualifying for duty-free status.
But Canada's minister of foreign affairs, Chrystia Freeland, said that "once the bilateral issues get resolved, Canada will be joining the talks to work on both bilateral issues and our trilateral issues".
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Before the president's announcement, Lightizer and Mexican Secretary of Economy Idelfonso Guajardo walked together into the White House without talking to reporters. That issue was a key request of the US, which has long wanted Canada and Mexico to raise their de minimis levels. But Prime Minister Justin Trudeau has insisted his government will only sign a deal that's good for Canada.
Trump says that on Friday, the Mexican deal will go to the lawmakers.
Trump has rejected other multi-national deals, such as the Trans-Pacific Partnership (another trade pact) and the Paris Agreement on climate change mitigation, expressing a strong preference for one-on-one negotiations on trade and other matters with countries.
Trump repeatedly criticized NAFTA, calling it "the worst trade deal in history".
The president hailed the preliminary pact as a "big deal" in a Monday morning tweet, but - at least for now - it does not include Canada.
Some experts interpreted the administration's signaling about a possible bilateral deal as an attempt to pressure Canada into a swift agreement on revising NAFTA, which the U.S. administration denied.
For that to happen, the US Congress must be notified 90 days in advance, which means the administration must send the notice by the end of the week.
"It will be necessary for Canada to rejoin the negotiations and for an agreement to be reached among all parties before a judgement can be made".