The Republican front-runner's proposed ban would apply to immigrants and visitors alike, a sweeping prohibition affecting all adherents of a religion practiced by more than a billion people worldwide. He said in a statement such a ban should stand "until our country's representatives can figure out what is going on."
"Until we are able to determine and understand this problem and the dangerous threat it poses, our country cannot be the victims of horrendous attacks by people that believe only in jihad, and have no sense of reason or respect for human life," he said.
Trump's 2016 presidential campaign has been marked by a pattern of inflammatory statements and he kicked off his campaign with a speech in which he said some Mexican immigrants are rapists and criminals. He recently drew criticism for retweeting an image of inaccurate statistics that vastly overrepresented the number of whites killed by blacks. But so far those and other errors of fact have not diminished his popularity among many Republican voters.
At an evening rally in South Carolina, Trump supporters cheered and shouted in support as he read his statement and warned that without drastic action, "it's going to get worse and worse, you're going to have more World Trade Centers."
Rod Weader, a 68-year-old real estate agent from North Charleston who attended the rally and said he agreed with Trump's plan "150 percent."
"As he says, we have to find out who they are and why they are here," he said.
Since the Nov. 13 attacks in Paris that killed 130 people and wounded hundreds more, a number of Republican presidential contenders have proposed restrictions on Syrian refugees - with several suggesting preference for Christians seeking asylum - and tighter surveillance in the US.
But Trump's proposed ban goes much further, and his Republican rivals were quick to reject the latest provocation from a candidate who has delivered no shortage of them. "Donald Trump is unhinged," former Florida governor Jeb Bush said via Twitter. "His 'policy' proposals are not serious."
John Kasich slammed Trump's "outrageous divisiveness," while a more measured Ted Cruz, who has always been cautious about upsetting Trump's supporters, said, "Well, that is not my policy."
Trump's plan also drew criticism from the heads of the Republican Party in Iowa, New Hampshire and South Carolina, the first three states to vote in next year's presidential primaries.
"It is un-Republican. It is unconstitutional. And it is un-American," said Jennifer Horn, chairwoman of the Republican Party of New Hampshire.
Trump campaign manager Corey Lewandowski said Trump's proposed ban would apply to "everybody," including Muslims seeking immigration visas as well as tourists seeking to enter the country.
In an interview on Fox News, Trump said Muslim members of the US armed forces would "come home" and that his plan would "not apply to people living in the country."
In the late 1800s, Congress passed legislation broadly aimed at halting Chinese immigration. But said Leti Volpp, a University of California expert on immigration law, "there is no precedent for a religious litmus test for admitting immigrants into the United States."
"Excluding almost a quarter of the world's population from setting foot in the United States based solely upon their religious identity would never pass constitutional muster," Volpp said.
Trump's proposal comes a day after President Barack Obama spoke to the nation from the Oval Office about the shootings in San Bernardino, California, which Obama said was "an act of terrorism designed to kill innocent people."
The FBI said Monday the Muslim couple who carried out the massacre had been radicalized and had taken target practice at area gun ranges, in one case within days of the attack last week that killed 14 people.