(Rewrites with comments from Paul Ryan on deadline for NAFTA agreement)

By David Ljunggren and Anthony Esposito

WASHINGTON, May 10 (Reuters) - U.S. House Speaker Paul Ryan has set a May 17 deadline to be notified of a new NAFTA trade deal to give the current Congress a chance of passing it, while Mexico's top trade official on Thursday said time was running short to meet such a deadline.

Ryan, who controls legislation in the House of Representatives, set his deadline in remarks delivered on Wednesday to the Ripon Society in Washington and publicized on Thursday.

Under the "fast track" trade negotiating law, there are lengthy notification periods before U.S. President Donald Trump could sign a new North American Free Trade Agreement and before Congress could begin considering it.

Letting negotiations drag on much longer would punt consideration to a new Congress elected in November that will take office in January 2018, one that could cede more control to Democrats.

"We have to have the paper -- not just an agreement, we have to have the paper -- from USTR by May 17 for us to vote on it this year, in December, in the lame duck" session, Ryan said.

A spokeswoman for Ryan said that he was referring to a notification of intent to sign the NAFTA agreement, not necessarily the full text.

Major differences remain between the three members of NAFTA after more than eight months of largely slow-moving negotiations launched at the insistence of President Trump, who wants major changes to the 1994 pact.

FRIDAY INDICATION

Mexico's Economy Minister Ildefonso Guajardo said he expected to learn by the end of Friday whether a new deal was possible. He and his counterparts have been meeting in Washington since Monday to try to bridge major gaps.

"I think we will be finding out through the day and tomorrow ... if we really have what it takes to be able to land these things in the short run," Guajardo told Reuters.

A source close to the talks said it was possible that Guajardo, U.S. Trade Representative Robert Lighthizer and Canadian Foreign Minister Chrystia Freeland could extend their meetings into the weekend.

A USTR spokeswoman declined comment while a Freeland spokesman did not respond to a request for comment.

Guajardo told Reuters that "we have suitcases for two weeks if necessary."

This week's talks hit an obstacle as the United States and Mexico sought to settle differences over the key issue of automobiles.

"Mexico obviously is here in order to negotiate the best agreement for Mexican workers and consumers. It will take as long as it will take," Mexican deputy economy minister Juan Carlos Baker told reporters late in the day.