Kenneth Smith, the head of Mexico's technical negotiating team, reiterated in a radio interview that from Mexico's perspective there are no fixed deadlines it is working towards.
"The possibility of having the entire negotiation done by Thursday isn't easy, we don't think it will happen by Thursday", Mexican Economy Minister Ildefonso Guajardo told the Televisa network, The Wall Street Journal reported.
Don't expect a NAFTA deal by this week's supposed target date.
Negotiators from the United States, Mexico and Canada have been in intense talks since late last month to try to reach a deal before upcoming US congressional elections.
"You have to continue to negotiate and the moment you reach a good negotiation, close the deal", he added.
Mexico had been pushing to secure at least the general terms of a deal before the Mexican presidential election on July 1.
Mexico's peso sank to its weakest in more than a year on Tuesday.
The three NAFTA partners, Mexico, Canada and the United States, continue to disagree on several issues, he said.
He even revealed the details of a conversation on the subject between Prime Minister Justin Trudeau and President Donald Trump, who spoke by phone on Monday.
Guajardo said he will continue in the negotiations but expressed discontent about the US request for the agreement to be renewed every five years, the Journal reported.
However, talks still faced the hurdles of US demands for a sunset clause that would allow NAFTA to expire if it is not renegotiated every five years, and the elimination of settlement panels for trade disputes.
"Mexico's position since the start of the negotiation has been that we're not going to sacrifice the quality of the deal to conclude quickly", he said, although he added that there is still time to reach a conclusion before the end of the year.
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.
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