Talks, however, remain hung up on key issues.
Adam Austen, Press Secretary for Canadian Foreign Affairs Minister Chrystia Freeland, said in a media statement that "the process of congressional ratification is internal to the USA", not a matter for Canada. There's no date for him to meet with Lighthizer and Freeland, Guajardo said.
"He's not going to stop until he gets it", she added.
If a NAFTA deal is not reached before the election, Mexico's negotiators will work closely with the incoming government's transition team, Smith told Mexican radio. However, the week is quickly coming to an end, and top trade negotiators from Mexico and Canada are not on-site with others this week.
Lighthizer is scheduled to attend meetings on Thursday and Friday with the Chinese vice premier, Liu He.
Kind said Lighthizer was "hopeful" that he could rebalance the trade agreement to ensure bipartisan support.
As negotiations have plodded on, Canada has sounded a more optimistic tone than Mexico.
The Mexican peso and Canadian dollar weakened following Lighthizer's comments.
Mexico's economy minister said a deal could be reached later this month, but left hope negotiations could still take place after the country's presidential election July 1.
Neymar To Real Madrid Would Be Terrible For Barcelona - Lionel Messi
Neymar has been heavily linked with a move to Real Madrid this summer after struggling to settle at Paris Saint Germain. It would be a huge blow for everyone. "It would make Real Madrid even stronger from a football point of view".
"An bad lot of things would have to go right in order for this to be voted on in this Congress", said Eric Miller, a Washington-based trade adviser and Woodrow Wilson Center fellow.
Mexican and Canadian officials on Thursday appeared to brush off the passage of an informal deadline set by the US Congress to reach a deal on revamping a continent-wide trade pact. "We can't work a bill unless we have an agreement that's in writing that we can work, and that hasn't occurred yet", Ryan told reporters in Washington.
Kevin Brady, the Republican chairman of the House Ways and Means Committee that has oversight over trade, this week also said there's not much wiggle room on May 17.
All three countries agreed that they would keep negotiating beyond Thursday, a date that had been presented as a procedural deadline for getting a deal to the U.S. Congress for a vote this year.
It rebuffed an effort from Prime Minister Justin Trudeau, Foreign Affairs Minister Chrystia Freeland, and several high-ranking staffers who were in the USA on Thursday urging a quick deal.
That is if the Trump administration wants Congress to consider an updated NAFTA before the end of 2018.
Trudeau drew another public contradiction Thursday - this one from Mexico.
"The state of play is uncertainty", said Maryscott Greenwood, chief executive officer of the Canadian American Business Council in Washington, which represents firms in both countries.
Canada and Mexico expressed continued resistance Thursday to the USA proposal for a so-called sunset clause that would kill NAFTA after five years unless all parties agree to extend it. Trudeau said the idea is still a sticking point, while Guajardo said it was out of the question.