Republican presidential candidate Donald Trump called Monday for a "total and complete shutdown of Muslims entering the United States" — the most dramatic response yet by a candidate to last week's shooting spree in San Bernardino, Calif., by what the FBI has called a radicalized couple.

The proposed ban would apply to immigrants and visitors alike, a sweeping prohibition affecting all adherents of Islam who want to come to the U.S. The idea faced an immediate challenge to its legality and feasibility from experts who could point to no formal exclusion of immigrants based on religion in America's history.

Trump's campaign said in a statement that such a ban should stand "until our country's representatives can figure out what is going on." It said the proposal comes in response to a level of hatred among "large segments of the Muslim population" toward Americans.

"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," Trump said in the statement.

At an evening rally in South Carolina, Trump supporters cheered and shouted in support as he read his statement. Trump warned during his speech that without drastic action, the threat of attacks is "going to get worse and worse."

GOP rivals quickly blast proposal

Since the Paris terrorist attacks, 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 U.S.

But Trump's proposed ban goes much further than those ideas, 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," Jeb Bush said via Twitter. "His 'policy' proposals are not serious."

Carly Fiorina said: "Trump's overreaction is as dangerous as President Obama's under-reaction."

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."

GOP 2016 Trump

Republican presidential candidate, businessman Donald Trump speaks during a rally coinciding with Pearl Harbor Day at Patriots Point aboard the aircraft carrier USS Yorktown in Mt. Pleasant, S.C.. (Mic Smith/Associated Press)

Ben Carson said he would not advocate "being selective on one's religion" but does believe that "everyone visiting our country should register and be monitored during their stay."

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.

New Hampshire GOP's chairwoman Jennifer Horn said the idea is "un-Republican. It is unconstitutional. And it is un-American," while South Carolina chairman Matt Moore said on Twitter, "As a conservative who truly cares about religious liberty, Donald Trump's bad idea and rhetoric send a shiver down my spine."

'Disturbing to all Americans'

Ibrahim Hooper, director of the Council on American-Islamic Relations (CAIR), also had a blistering response.

"We're entering into the realm of the fascist now," he said. "It should be disturbing not only to American-Muslims, but it should be disturbing to all Americans that the leading Republican presidential candidate would issue essentially a fascist statement like this."

Trump campaign manager Corey Lewandowski says Trump's proposed ban would apply to "everybody," including Muslims seeking immigration visas and tourists seeking to enter the country.

His campaign did not immediately respond to questions about whether it would also include Muslims who are U.S. citizens and travel outside of the country, or how a determination of someone's religion might be made by customs and border officials.

There are, for example, more than 5,800 servicemen and women on active U.S. military duty and in the reserves who self-identify as Muslim and could be assigned to serve overseas. Trump said later Monday in an interview on Fox News: "They'll come home."

Trump was also unclear on whether his ban would apply to Muslim allies in the fight against Islamic State militants.

Trump's proposal comes a day after U.S. President Barack Obama spoke to the nation from the Oval Office in the wake of the shootings in San Bernardino, Calif., which Obama called "an act of terrorism designed to kill innocent people."

The FBI said Monday that the couple who carried out the massacre had been radicalized and had attended target practices at local gun ranges, including one days before the deadly attack that killed 14 people.

Trump's campaign has been marked by a pattern of inflammatory statements, dating back to his harsh rhetoric about Mexican immigrants. He has taken a particularly hard line against Muslims in the days since the Paris attacks, advocating enhanced surveillance of mosques due to fears over radicalization.

White House spokesman Josh Earnest accused Trump of playing on people's fears and trying to tap into "a darker side, a darker element" of American society.

From the Democratic presidential campaign, Bernie Sanders said "Trump and others want us to hate all Muslims" and Hillary Clinton called the proposal "reprehensible, prejudiced and divisive."

On Capitol Hill, Republican Sen. John McCain, of Arizona, said: "It's just foolish."

But will it hurt Trump in the campaign? "I have no idea," McCain said. "I thought long ago that things he said would hurt his prospects, and he continues to go up."

For some Republicans, the most pressing challenge isn't keeping Trump from negatively branding Republicans in the general election — it's making sure he's not the candidate representing the party in next November's White House race.

"So far, every boundary he has pushed has worked out for him," said Ari Fleischer, who served as White House press secretary for former President George W. Bush. "I hope GOP voters recognize this time he's gone too far."

With files from Reuters