Donald Trump doubled down on his controversial hard-line policy proposals on illegal immigration and border security Wednesday in a tough-talking speech unlikely to broaden his appeal to moderate voters.

The Republican Party candidate for president laid out a 10-point plan in which he promised to deport 2 million people he described as "criminal aliens," increase border patrols and assign a new "deportation task force," as well as cancel executive orders signed by US President Barack Obama that currently protect some undocumented immigrants from deportation.

As the crowd in Phoenix in the south-western border state of Arizona roared, Trump reprised his signature proposal.

"On day one, we will begin working on an impenetrable, physical, tall, powerful, beautiful southern border wall," he said, adding that Mexico would foot the bill.

"They don't know it yet, but they're going to pay for it," he said.

The billionaire mogul, whose wife is an immigrant from Slovenia, peppered his policy proposals with appeals to xenophobia.

He suggested the US should vet immigrants based on their perceived ability to assimilate, and claimed "most" of the estimated 11 million undocumented immigrants in the US are "low-skilled" people who "draw more from the system than they can ever pay back."

He proposed closing the door to war refugees from Syria and other states, suggesting they were a "Trojan horse" danger to public security.

"We have no idea who they are, where they come from - it's going to end badly, folks, it's going to end badly," he said.

In closing, he brought onstage women who told stories of loved ones they said had been killed by undocumented immigrants.

The highly anticipated speech ended speculation that Trump was considering softening his stance on immigration enforcement, after he had floated the possibility of legalizing some of the estimated 11 million undocumented immigrants in the US earlier in the week.

Trump is trailing his Democratic rival Hillary Clinton in opinion polls, reliant on support from white men that may not be enough to win the election.

Influential elections handicapper FiveThirtyEight has Clinton leading Trump by about five points in the popular vote, and estimates she has a 74 per cent change of winning in November.

Many analysts have suggested his only hope of narrowing the gap is to broaden his appeal to women and non-white people.

The speech capped a day in which Trump traveled to Mexico for a a hastily arranged meeting with Mexican President Enrique Pena Nieto, who drew fire at home for extending an invitation that was widely condemned by Mexicans angry at Trump's history of anti-Mexican rhetoric.

Pena Nieto emphasized that he had invited Trump's Democratic opponent Hillary Clinton as well for discussions about future bilateral relations.

At a joint press conference after their meeting, the two men appeared cordial and succinct, but stuck to their guns on policy.

Pena Nieto emphasized bilateral benefits to the US-Mexico trade relationship and cross-border challenges beyond immigration to the US from Mexico, among them the flow of illegal guns and cash from the US to Mexican drug cartels.

He stood up for Mexican immigrants, calling them honest and "hard-working" people who deserved respect.

On that point, at least, Trump agreed. In contrast to his past depictions of Mexican immigrants as criminals and rapists, Trump praised Mexican-Americans as "spectacular" and "beyond reproach," citing his experiences with many who work for him in the hotels that bear his name.

But he took issue with Pena Nieto's characterization of the cross-border relationship, saying the North American Free Trade Agreement had benefited Mexico more that the United States, which he said has suffered a "tremendous outflow of jobs."

Media attention to the substance of the meeting quickly turned to the two men's conflicting accounts of their discussions of Trump's proposed border wall.

Directly after the meeting, Trump told press he had not discussed the subject of who would pay for the wall with the Mexican leader.

Later, Pena Nieto insisted on Twitter he had made it clear at the beginning of the meeting that Mexico "will not pay."

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