Donald Trump vowed that Mexico will fully pay for the border wall in a speech focused on immigration.
Hours earlier, he met Mexican President Enrique Pena Nieto but said they had not discussed financing the wall.
The president later insisted he had told Mr Trump Mexico would not pay.
There had been speculation that the Republican candidate would back off his plan to deport the estimated 11m undocumented immigrants living in the US.
In his speech in Phoenix, there were conflicting signals about this. He said their fate was not a “core issue” and that deporting “criminal aliens” would be the priority.
“We will treat everyone living or residing in our country with great dignity,” he said.
But later he struck a more uncompromising note when he added: “Anyone who has entered the United States illegally is subject to deportation. That is what it means to have laws.”

In a fiery speech that was at odds with his softer tone in Mexico City, he said he would:
- Create a “special deportation force” focused on removing immigrants arrested (not convicted) for crimes
- Cut off any path to citizenship and insisted those seeking legal status must return to their own countries first
- Introduce “extreme vetting” of immigrants to make sure they adhered to American values
- Protect the interests of African American and Hispanic workers by restricting legal immigration numbers
- Get tough on people who overstay their visas, making them subject to deportation
Mr Trump said it was the right of the US to choose immigrants that “we think are the likeliest to thrive and flourish and love us”.
Elaborating on that idea, he said his “extreme vetting” would involve an ideological test for immigrants applying to live in the US.
“Applicants will be asked
Mr Trump, a New York hotel developer, stormed to an unlikely victory in the Republican primaries partly due to his tough talking on immigration.
During a speech in Phoenix, Trump promised to protect the interests of Americans affected by immigration. He voiced concerns about immigration’s impact on jobs, wages, housing, schools, taxes, and living conditions. Trump accused Clinton of supporting amnesty and criticized her for advocating open border policies. Clinton criticized Trump for not discussing payment for the border wall during his visit to Mexico, stating that he had “choked.”