Donald Trump has vowed to deport millions of people in his "first hour" of office if he becomes president at the end of a day in which he stoked tensions with Mexico over the issue of immigration and who would pay for a border wall.

Seeking to end confusion over his aggressive but muddled language on immigration, he vowed to remove those living in the country illegally if he becomes president, warning that failure to do so would jeopardise the "well-being of the American people."

He also vowed to create a special "deportation force" that would seek to remove all who didn't have permission to live and work in the country.

"Anyone who has entered the United States illegally is subject to deportation. We will begin moving them out, day one. My first hour in office, those people are gone.”

He added: "There will be no amnesty."

He also told the crowd that he would introduce "extreme vetting" of immigrants.

Mr Trump was speaking in Phoenix hours after his controversial trip to Mexico in which the billionaire businessman met Mexican President Enrique Peña Nieto over the building of a border wall between the two countries.

The two had held a private meeting on Wednesday afternoon, followed by a joint press conference where Mr Trump said the issue of a border wall did come up but that they did not talk about who would foot the bill.

But Mr Nieto later contradicted the Republican candidate, and said that he “made it clear” that Mexico will not pay for the wall the New York tycoon wants to build.

Donald Trump's most controversial quotes Show all 14 1 /14 Donald Trump's most controversial quotes Donald Trump's most controversial quotes On Isis: "Some of the candidates, they went in and didn’t know the air conditioner didn’t work and sweated like dogs, and they didn’t know the room was too big because they didn’t have anybody there. How are they going to beat ISIS?" Getty Donald Trump's most controversial quotes On immigration: "I will build a great wall — and nobody builds walls better than me, believe me —and I’ll build them very inexpensively. I will build a great, great wall on our southern border, and I will make Mexico pay for that wall. Mark my words." Reuters Donald Trump's most controversial quotes On Free Trade: "Free trade is terrible. Free trade can be wonderful if you have smart people. But we have stupid people." PAUL J. RICHARDS | AFP | Getty Images Donald Trump's most controversial quotes On Mexicans: "When Mexico sends its people, they’re not sending their best. They’re sending people that have lots of problems. They’re bringing drugs. They’re bringing crime. They’re rapists." Getty Donald Trump's most controversial quotes On China: "I just sold an apartment for $15 million to somebody from China. Am I supposed to dislike them?... I love China. The biggest bank in the world is from China. You know where their United States headquarters is located? In this building, in Trump Tower." Getty Images Donald Trump's most controversial quotes On work: "If you're interested in 'balancing' work and pleasure, stop trying to balance them. Instead make your work more pleasurable." AP Donald Trump's most controversial quotes On success: "What separates the winners from the losers is how a person reacts to each new twist of fate." Donald Trump's most controversial quotes On life: "Everything in life is luck." AFP Donald Trump's most controversial quotes On ambition: "You have to think anyway, so why not think big?" Getty Images Donald Trump's most controversial quotes On his opponents: "Bush is totally in favour of Common Core. I don't see how he can possibly get the nomination. He's weak on immigration. He's in favour of Common Core. How the hell can you vote for this guy? You just can't do it." Reuters Donald Trump's most controversial quotes On Obamacare: "You have to be hit by a tractor, literally, a tractor, to use it, because the deductibles are so high. It's virtually useless. And remember the $5 billion web site?... I have so many web sites, I have them all over the place. I hire people, they do a web site. It costs me $3." Getty Images Donald Trump's most controversial quotes On Barack Obama: "Obama is going to be out playing golf. He might be on one of my courses. I would invite him. I have the best courses in the world. I have one right next to the White House." PA Donald Trump's most controversial quotes On himself: "Love him or hate him, Trump is a man who is certain about what he wants and sets out to get it, no holds barred. Women find his power almost as much of a turn-on as his money." Getty Images Donald Trump's most controversial quotes On America: "The American Dream is dead. But if I get elected president I will bring it back bigger and better and stronger than ever before and we will make America great again." GETTY

“At the beginning of the conversation with Donald Trump,” the Mexican president tweeted. “I made it clear that Mexico will not pay for the wall.

Mr Nieto, speaking on TV shortly after, went on the offensive still further, saying Trump posed a threat to his country: "His policy stances could represent a huge threat to Mexico, and I am not prepared to keep my arms crossed and do nothing," he said.

"That risk, that threat, must be confronted. I told him that is not the way to build a mutually beneficial relationship for both nations."

And relations between the pair plunged even further when Mr Trump, just hours later, rowed back on his seemingly conciliatory tone earlier by insisting "100%" that Mexico would pay for the wall.

The Hillary Clinton campaign bashed Donald Trump’s last-minute visit to Mexico, and said “he got beat in the room and lied about it”.

“Donald Trump has made his outlandish policy of forcing Mexico to pay for his giant wall the centrepiece of his campaign,” said Hillary for America chair John Podesta. “But at the first opportunity to make good on his offensive campaign promises, Trump choked.”

Donald Trump to run for US President

He continued: “What we saw today from a man who claims to be the ultimate ‘deal maker’ is that he doesn’t have the courage to advocate for his campaign promises when he’s not in front of a friendly crowd. We know who he is.”

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Prior to the appearance, Ms Clinton took aim at Mr Trump for his “dropping in” on Mexico.

“You don’t build a coalition by insulting our friends or acting like a loose cannon. You do it by putting in the slow, hard work of building relationships,” the former Secretary of State said at an event in Cincinnati.