"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.
He added on Twitter: "Just put out a very important policy statement on the extraordinary influx of hatred & danger coming into our country. We must be vigilant!"
Trump's remarks, coming days after the terror attack in San Bernardino, California, revived a campaign 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 and saying he would support requiring all Muslims in the United States to be registered in a special database, which his critics have likened to the mandatory registration of Jews in Nazi Germany.
The nearly unanimous condemnation from fellow Republicans, Democrats and legal and immigration experts showed no sign of affecting Trump. He reiterated his proposal to keep Muslims out of the U.S. "until our country's representatives can figure out what is going on" at a Monday night rally in South Carolina, drawing cheers from the crowd.
But this proposal may have crossed a line. "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."
On Monday night, while there was some positive response to Trump's latest remarks — conservative pundit Ann Coulter tweeted "GO TRUMP, GO!" — repudiation of Trump's latest comments came swiftly, forcefully and from many quarters. Social media reaction led hashtags such as #racism, #fascism and #bigot to trend heavily and condemnation went global.
"He's trying to alienate not only the Muslim population of the United States but all the Muslims around the world," said Ikebal Patel, former president of the Australian Federation of Islamic Councils. "Nobody in their right mind would in any way condone what has just happened with those two individuals in that town, but to condemn in one fell swoop all the Muslims and to try to suggest that Muslims shouldn't be allowed in America is quite ridiculous."
Nihad Awad, national executive director of the Council on American-Islamic Relations (CAIR) blasted Trump. “This is outrageous coming from someone who wants to assume the highest office in the land," said Awad. "It is reckless and simply un-American."
Several of Trump's Republican rivals quickly rejected the latest provocation.
"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 Texas Sen. Ted Cruz, who has always been cautious about upsetting Trump's supporters, said, "Well, that is not my policy."
"Everyone visiting our country should register and be monitored during their stay as is done in many countries," said Ben Carson, retired neurosurgeon and GOP candidate for president. "I do not and would not advocate being selective on one's religion."
Dick Cheney, the former vice president said, "Religious freedom has been a very important part of our history and where we came from. ... It's a mistaken notion."
Trump's comments Monday came as his lead in preference polls in Iowa, the state that kicks off the nominating contest, appeared to be challenged by Cruz. If Trump's goal was to shift focus away from Cruz and back onto his candidacy, he no doubt succeeded.
Trump's comments seem aimed squarely at Republican primary voters wary of Muslims, particularly those with direct ties to countries in the Middle East that have spawned violent extremist groups.
A 2014 Pew Research Center poll showed Republicans view Muslims more negatively than they do any other religious group, and significantly worse than do Democrats.
The Islamophobic card is one Trump's rival have been willing to play.
In September, Carson said he did not believe a Muslim should serve as president of the United States. "I would not advocate that we put a Muslim in charge of this nation. I absolutely would not agree with that," Carson said in an interview with NBC's "Meet The Press."
After the recents attacks in Paris, which left 130 people dead and hundreds more wounded, GOP candidates rallied to the idea of blocking Syrian refugees from entering the United States.
Cruz proposed legislation banning Syrian Muslims from coming to the U.S. Bush said American assistance to Syrian refugees should focus primarily on Christians. And Carson compared handling refugees fleeing Syria's intractable civil war to dealing with "rabid dogs."
Republican governors balked at having Syrian refugees resettled in their states.
The pile-on became so charged, President Barack Obama lashed out at the Republicans, deeming their words offensive and insisting “it needs to stop.”
On Wednesday, 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.
He did not 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.
In response to a request for additional detail, Trump said via a campaign spokeswoman: "Because I am so politically correct, I would never be the one to say. You figure it out!"
Trump's proposal comes a day after 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.
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. The United States is a great nation when we stand together. We are a weak nation when we allow racism and xenophobia to divide us."
Al Jazeera and wire services