US Republican presidential candidate Donald Trump on Wednesday delivered a speech describing his vision on illegal immigration in which he dismissed current policies as "weak and foolish."

"There is only one core issue in the immigration debate, and that issue is the well-being of the American people," he said to rapturous applause. "Nothing even comes in close second."

The real estate mogul laid out what he called a ten-point plan to put an end to irregular migration, including bolstering US Immigration and Customs Enforcement (ICE) border personnel and deporting thousands of so-called illegal migrants.

"Under my administration, anyone who illegally crosses the border will be indefinitely detained until they are returned to where they came," Trump told supporters in Phoenix, Arizona.

The American billionaire committed to blocking all paths for illegal migrants to obtain legal status in the US.

"Our message to the world will be this: you cannot obtain legal status or become a citizen of the United States by illegally entering our country," he said. "There will be no amnesty."

Trump also criticized Democratic presidential candidate Hillary Clinton's call to boost the number of Syrian refugees hosted in the US, saying he would freeze all visas for people originating in countries where "adequate screening cannot occur.

An "ideological certification" exam would also be provided to potential legal migrants to ensure "they share our values and love our people."

The speech comes on the heels of a closed-doors meeting between Trump and Mexican President Enrique Pena Nieto earlier on Wednesday.

Sizing up the wall

The Republican presidential candidate claimed that both politicians discussed his proposed border wall to curb migration, but did not talk about who will pay for it. Trump had previously claimed that Mexico would foot the bill for the controversial measure.

Nieto later said in a tweet that he explicitly told Trump that Mexico would not pay for the construction of a wall on its border with the US, contradicting Trump's statement that neither of them discussed how it would be financed.

Trump's Democrat challenger, Hillary Clinton, tweeted that her opponent "failed" in his first diplomatic foray.

However, Trump doubled down on his promise during his immigration speech in Phoenix. "We will build a great wall along the southern border, and Mexico will pay for the wall - one hundred percent," he said.

Trump's speech comes just over ten weeks before Americans head to the polls to vote for the next president.

ls/gsw (AP, AFP, Reuters)