(AP) -- Seeking to end confusion over his aggressive but recently muddled language on immigration, Donald Trump vowed Wednesday to remove millions of people living in the country illegally if he becomes president, warning that failure to do so would jeopardize the "well-being of the American people."

But Trump didn't address what he would do about millions more who might remain under his approach -- the major question that has frustrated past congressional attempts at remaking the nation's immigration laws.

Instead, Trump repeated the standard Republican talking point that only after securing the border can such a discussion begin to take place.

It was a retreat in the rhetoric for the billionaire from the GOP primaries, when he had vowed his "deportation force" would seek to remove all who didn't have permission to live and work in the country.

The Republican presidential candidate insisted than any of the estimated 11 million such immigrants who want to seek legal status or citizenship in the United States must return to their home countries in order to do so. And he outlined plans to create a special task force that would prioritize the deportation of criminals, people who have overstayed their visas and other immediate security threats.

"Anyone who has entered the United States illegally is subject to deportation," Trump charged in the highly anticipated speech, which took place hours after he met with Mexican President Enrique Pena Nieto.

He added, "There will be no amnesty."

The aggressive tone during his speech in Phoenix marked a shift from the New York billionaire's demeanor earlier in the day, when a much more measured Trump described Mexicans as "amazing people" as he appeared alongside Pena Nieto in Mexico's capital city. It was his first meeting with a head of state as his party's presidential nominee.

Shortly after the joint appearance, a dispute arose over the most contentious part of the billionaire's plans to secure the U.S. southern border and fight illegal immigration -- his insistence that Mexico must pay to build his promised wall.

Trump told reporters during the afternoon appearance that the two men didn't discuss who would pay for a cost of construction pegged in the billions. Silent at that moment, Pena Nieto later tweeted, "At the start of the conversation with Donald Trump I made it clear that Mexico will not pay for the wall."

With the meeting held behind closed doors, it was impossible to know who was telling the truth. But clash cast a cloud over Trump's first meeting with a foreign dignitary and threatened to overshadow the evening address.