Marco Rubio, who faces a do-or-die contest in Florida on March 15, said Islam had a problem with radicalization but said that many Muslims were proud Americans.
“Presidents can’t just say whatever they want. It has consequences,” he said, to cheers from the audience.
The four Republicans heeded pleas from party leaders to have a civil debate.
Unlike in the last TV event, which was littered with personal insults, this one was more substantive with a focus on policy.
“So far, I cannot believe how civil it’s been up here,” Donald Trump observed at one point.
However, on the issue of Islam, there was clear distance between Donald Trump and the others. The billionaire stood by comments he made earlier in the day when he said “Islam hates us, there’s a tremendous hatred”, and railed against political correctness.
Marco Rubio said: “I’m not interested in being politically correct. I’m interested in being correct.”
All three of Donald Trump’s rivals distanced themselves from Trump’s statement in December that in the fight against terrorist “you have to take out their families”.
“We’ve never targeted innocent civilians and we’re not going to start now” Ted Cruz said.
When Donald Trump was challenged on the legality of targeting civilians, he said that America had to be able to fight on “an equal footing”.
“We have to obey the laws, but we have to expand those laws,” he said.
On March 15, five large states will vote for presidential candidate in each party, with Ohio Governor John Kasich and Marco Rubio, a Florida senator, under pressure to win their home states.
Donald Trump picked up a key endorsement of Ben Carson, who last week dropped out of the race before the debate.
The candidates also clashed over President Barack Obama’s historic visit to Cuba next week.
Marco Rubio, whose parents were Cuban immigrants, said he was opposed to efforts to restore relations until Cuba improved its human rights record.
However, Donald Trump said he was not opposed to a US-Cuba deal, but it should be on better terms for the US.
The other Cuban-American candidate on the stage, Ted Cruz, accused Donald Trump of supporting the Obama-Clinton policy on Cuba.
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