May 17 loomed as a deadline for a preliminary agreement after Paul Ryan, the speaker of the U.S. House of Representatives, last week said that for Congress to approve a revamped NAFTA, an agreement in principle had to be submitted by then.
Ryan himself told reporters at the U.S. Capitol that Congress can not begin working on the negotiating law known as "fast track" without a trade deal in hand.
United States House Speaker Paul Ryan set the cut-off date last Wednesday amid some optimism that Mexico, the US and Canada could soon reach an agreement in principle as a result of meetings attended last week by the chief trade representatives in Washington.
"The possibility that by Thursday we will have all of the negotiation (wrapped up) is not likely".
Leftist Andres Manuel Lopez Obrador is leading polls to win the Mexican presidential race.
"You have to continue to negotiate and the moment you reach a good negotiation, close the deal", he added.
But Canadian Prime Minister Justin Trudeau struck a more upbeat tone, telling reporters in Calgary a few hours later, "There is very much an eminently achievable outcome. and we are very close".
A report in Canadian media said Trudeau make a direct appeal to Trump to keep momentum alive at the negotiating table.
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Chief Mexican NAFTA negotiator Kenneth Smith said that the administration of President Enrique Pena Nieto had a responsibility to keep negotiating until Mexico's new president, who will be elected on July 1, takes office on December 1.
In the five-month period between election day and the swearing-in ceremony, Guajardo said, the next government's team would need to be involved in any ongoing trilateral trade talks.
However, the trio may be closer to agreeing on automotive rules of origin that place caps on the amount of foreign-made parts allowed in vehicles manufactured in North America, said Guajardo.
Guajardo said it was not yet clear when the ministers from Mexico, Canada and the United States responsible for negotiating NAFTA would meet again.
"We could see the elements to arrive at a balanced agreement".
More flexibility was needed for a deal, Guajardo said.
Officials from Canada and Mexico were in D.C. last week working on the terms of a deal, but nothing was reached.
Mexico's top trade negotiator said Tuesday that he doesn't believe an agreement between his country, the US and Canada will be reached by Thursday's informal deadline.