In a live television debate, two of his Republican rivals, who are also fighting for presidential nomination, John Kasich and Jeb Bush, were very critical of Mr Trump’s immigration plans.
Mr Trump, a billionaire New Yorker who has been leading in the polls, was booed as he tried to counter-attack.
Another source of friction at the debate in Milwaukee was foreign policy.
The eight candidates were divided on whether the US should do more to intervene in the Middle East, especially in the fight against Islamic State (IS) militants.
But immigration sparked the biggest confrontation when Mr Trump said that a wall should be built at the US-Mexico border, and all migrants living illegally in the US must be deported.