Even in private, Trump did not apologize to Pena Nieto, presidential spokesman Eduardo Sanchez said.

Trump is trailing Democratic rival Hillary Clinton in opinion polls for the Nov. 8 election. The New York businessman's aides hoped the trip would make him look presidential and show he is willing to deal head on with a thorny issue like relations with Mexico.

The scenes of a measured Trump meeting with a foreign leader were aimed at convincing moderate American voters to see him in a more positive light as he tries to broaden his appeal.

Trump's visit to Mexico City took place hours before he was due to deliver a highly anticipated speech in the US border state of Arizona on how he will tackle illegal immigration if he wins the election.

Trump has been pilloried in Mexico since he launched his White House campaign last year.

He has pledged to renegotiate or scrap the 1994 North American Free Trade Agreement trade deal between the United States, Mexico and Canada.

Clinton, a former secretary of state, said on Wednesday that Trump could not paper over his previous harsh language against Mexico, which helped him defeat 16 rivals for the Republican presidential nomination.

"It certainly takes more than trying to make up for more than a year of insults and insinuations by dropping in on our neighbors for a few hours and then flying home again," she told a convention of the American Legion military veterans' group in Cincinnati.