MEXICO CITY—Mexico’s chief trade negotiator said Tuesday that he doesn’t expect talks on the North American Free Trade Agreement to be wrapped up by Thursday, increasing the likelihood that a new Nafta won’t be voted on by the current U.S. Congress.

“The possibility of having the entire negotiation done by Thursday isn’t easy, we don’t think it will happen by Thursday,” Economy Minister Ildefonso Guajardo told the Televisa network.