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The real estate developer and reality TV star said during a debate in Las Vegas that his proposal is not about religion, but about security.
Trump added that any foreign Muslims who arrived in the country during the Obama administration “are leaving. They are going. They’re gone” if he becomes president.
Trump said voters are concerned about illegal immigration and his comments have “opened up a very big discussion that needed to be opened up”.
At least one other Republican presidential candidate attacked Trump. Former Florida governor Jeb Bush called him a “chaos candidate” and said it is not a serious proposal.
“It will push the Arab world away from us at a time when we need to engage with the Arab world,” Bush said.
Debate
Republican presidential candidates were taking part in their fifth and final televised debate on Tuesday prior to the first rounds of voting in the party primaries.
Nine of the 13 candidates actively seeking the Republican nomination took the stage in Las Vegas to face questions on foreign policy by CNN journalists. It was the first debate since the terrorist attacks in Paris and San Bernardino, California, changed the tone of the campaign.
Trump was positioned at centre stage based on his frontrunner status. He was flanked by retired neurosurgeon Ben Carson and Texas Senator Ted Cruz, who follow Trump in opinion polls.
The other six participants are Florida Senator Marco Rubio, Bush, businesswoman Carly Fiorina, New Jersey Governor Chris Christie, Ohio Governor John Kasich and Kentucky Senator Rand Paul.
In one poll, Cruz surged to the front of the pack with 31% support among voters likely to attend the Republican caucuses in Iowa. It was published on Saturday by Bloomberg and the Des Moines Register.
That poll placed Trump a distant second at 21% among caucus voters. Cruz also leads a Fox News poll issued on Sunday with 28% to 26% for Trump.
But a nationwide poll released on Tuesday by the Washington Post and ABC News showed Trump has increased his lead in the Republican primary to its largest margin yet.
That poll put Trump’s support at 38% among registered Republicans and GOP-leaning independents, six points higher than in October and November. Cruz surged into second in the poll with 15%.
Voting begins in less than two months. Iowa caucuses on February 1 and the New Hampshire primary on February 9 are the states with the earliest polls.
Four other candidates, who have too little support in opinion polls to qualify for the prime-time stage, took part in what is being called the under card debate. They are former Arkansas Governor Mike Huckabee, former Pennsylvania Senator Rick Santorum, former New York Governor George Pataki and South Carolina Senator Lindsey Graham.
