Donald Trump's hardline stance on immigration after two bombings in the New York area again sparked debate on the White House campaign trail Tuesday, as his son caused a firestorm by comparing Syrian refugees to lethal candies.

The Republican presidential hopeful's uncompromising position on undocumented migrants -- even calling them a dangerous "Trojan horse" who enter the country with the aim of doing harm -- is inextricably linked to his meteoric political rise.

Most Republicans approve of his tough talk, with polls showing that a majority of party members agreed with his call last December to bar Muslims from entering the United States.

Since then, Trump has refrained from specifically targeting Muslims, but he has championed police profiling of suspects and promised to bar immigrants and travellers from certain countries deemed dangerous, such as Syria.

"We want to make sure we are all only admitting people in our country who love our country," he said Tuesday in a speech at High Point University in North Carolina.

"It's just a plain fact that our current immigration system makes no real attempt to determine the views of the people entering our country. We have no idea who they are, what they think," he said.

Trump also denounced the "open borders" that he said his Democratic rival Hillary Clinton advocated as secretary of state, blaming her for the rise of the Islamic State group.

"All these disasters with ISIS happened on Hillary Clinton's watch, happened with her, her bad judgment, her bad decision-making," he said.

Immigration is not one of the major issues on the minds of voters, ranking fourth according to a recent CBS/New York Times poll, making it unclear if Trump, 70, can use it to persuade those who are still undecided.