Donald Trump has told Mexico's president the US "reserves the right" to build a wall along the border with its southern neighbour.

In a joint press conference with President Enrique Pena Nieto in Mexico City, Mr Trump defended his plan as a "sovereign right and mutually beneficial" to both Mexico and the US.

In his first overseas visit as Republican presidential nominee, Mr Trump said his oft-stated vow to make Mexico pay for such a structure was not covered during their meeting.

"We did discuss the wall, we didn't discuss payment of the wall, that will be at a later date, this was a very preliminary meeting, it was an excellent meeting," the New York businessman said.

The property magnate, who has previously labelled some illegal Mexican migrants rapists and criminals, struck a more diplomatic tone on Wednesday, describing his visit as a "great honour".

Standing at a podium flanked by his host, Mr Trump also told reporters: "I happen to have tremendous feeling for Mexican Americans ... they are amazing people."

Mr Pena Nieto said they had had a "very open and constructive discussion" about the border issue and trade between the US and Mexico.

The Mexican leader said undocumented immigration from Mexico to the US had dropped considerably since reaching a peak a decade ago.

The visit is something of a surprise - not least because Mr Pena Nieto has likened the White House hopeful to Adolf Hitler and Benito Mussolini.

Mr Trump has hardly endeared himself by accusing Mexico of sending violent offenders to the US, vowing to bill Mexico for a 2,000-mile wall along America's southern border, and threatening to tear up the North American Free Trade Agreement.

Senior Mexican officials appeared taken aback that the bombastic real estate baron had accepted their invite.

Mr Pena Nieto's compatriots have rained criticism upon him for courting the Manhattan real estate baron - something of a hate figure to many in Mexico.

The Mexican president, whose approval ratings had already sunk to 23%, defended his move by tweeting that he believes in dialogue to promote Mexico's interests.

Mr Pena Nieto also invited Democratic presidential candidate Hillary Clinton, but her campaign has not yet responded.