President of Mexico Enrique Pena Nieto (L) welcomes US Republican presidential candidate Donald Trump, in Los Pinos, Mexico City, Mexico, 31 August 2016.

Following a hastily arranged meeting with President Enrique Pena Nieto in Mexico City, Donald Trump on Wednesday praised Mexican-Americans while calling it a "sovereign right" for a country to secure its border, even with a wall.

Trump, the US presidential nominee of the conservative Republican Party, accepted an invitation that Pena Nieto had likewise extended to Democratic candidate Hillary Clinton.

In a news conference, Trump said he had expressed his view to the Mexican president that the North American Free Trade Agreement had benefited Mexico more that the United States, which he said has suffered a "tremendous outflow of jobs."

The real estate billionaire said that both countries should work together to keep jobs and industries in the western hemisphere. Trump called Mexican-Americans "spectacular" and "beyond reproach," citing his experiences with many who work for him in the hotels that bear his name.

In a reference to his inflammatory campaign pledge last year to "build a wall" between the two countries and make Mexico pay for it, Trump said the wall was discussed but not who would pay for it.

Pena Nieto said that many Mexicans have been "offended" by the rhetoric in the US campaign. Mexicans are honest and "hard working people" who deserved respect, he said.

While noting that he was not in agreement with Trump on all topics, Pena Nieto agreed that NAFTA could be "improved."

The Mexican president also said that while many US citizens see undocumented immigration as a "real problem," the problem reached its zenith a decade ago and has since greatly diminished.

Both noted that with 1 million people legally crossing their shared border daily, and 500 billion dollars in trade annually, it was in both countries' interest to secure the border to stem the flow of undocumented immigrants and illegal drugs into the US, as well as illicit cash and weapons into Mexico, which is fighting notoriously brutal drug cartels.

The meeting came just hours before Trump was to deliver what has been billed as a major immigration policy speech in the border state of Arizona, scheduled for 6 pm (0100 GMT Thursday).

Many in Mexico decried the invitation ahead of the meeting.

The left-leaning Democratic Revolution Party (PRD) said in a statement that Pena Nieto had made "a grave mistake to let himself be used to serve Trump's electoral interests."

"Donald Trump is a person who has insulted and denigrated Mexicans, who has headed a campaign of hate against us and who has lied with the purpose of dividing the Mexican and US people," it said.

Conservative ex-president Vicente Fox said that the US magnate was not welcome and that Pena Nieto was running a serious risk by welcoming him. "[Trump] is using him to win Hispanic votes. I don't know why [Pena Nieto] invited him," he told Milenio TV.

The trip comes in an election season in which Trump had frequently derided Mexico.

Trump has been far from flattering in his descriptions of the US' southern neighbour, using Twitter to call the Mexican court system "corrupt" and warning, "Don't do business with Mexico!"

In another tweet Trump said, "I love the Mexican people, but Mexico is not our friend. They're killing us at the border and they're killing us on jobs and trade. Fight!"

Trump has made his hardline stance on immigration a central part of his campaign since he announced his candidacy and has drawn fire from critics for his vow to build a wall and for calling Mexican immigrants criminals.

He has repeatedly pledged to build a wall on the US-Mexico border that he said the Mexican government would pay for and called for the deportation of 11 million people.

However, in recent days the Trump campaign issued a series of mixed messages on the issue, one day suggesting a softening of his position with a possible plan to legalize millions of immigrants, while the next inviting relatives of people killed by illegal immigrants to appear at his rallies.

Reacting to Trump's Mexico trip announcement, the Clinton campaign reiterated that "From the first days of his campaign, Donald Trump has painted Mexicans as 'rapists' and criminals and has promised to deport 16 million people, including children and US citizens."

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