"I think that we should definitely disallow any Muslims from coming in. Any of them. The reason is simple: we can't identify what their attitude is," said 75-year-old Charlie Marzka of Myrtle Beach, South Carolina.

Moreover, the Muslim travel ban will likely do little to dent Trump's own popularity among Republican primary voters. The billionaire businessman has dominated the GOP contest for months despite repeated controversies that would likely sink other White House hopefuls.

"Without looking at the various polling data, it is obvious to anybody the hatred is beyond comprehension. Where this hatred comes from and why we will have to determine," Trump said in a statement. "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's campaign added in the release that such a ban should remain in effect "until our country's representatives can figure out what is going on."

The release pointed to an online poll from the controversial Center for Security Policy, which claimed that a quarter of Muslims living in the U.S. believe violence against Americans is justified as part of a global jihadist campaign. Critics have questioned the reliability of the organization's information.It also pointed to a Pew Research poll, which the campaign declined to identify, which the campaign claimed points to "great hatred towards Americans by large segments of the Muslim population."

Trump campaign manager Corey Lewandowski told CNN on Monday that the ban would apply not just to Muslim foreigners looking to immigrate to the U.S., but also to Muslims looking to visit the U.S. as tourists.

"Everyone," Lewandowski said when asked if the ban would also apply to Muslim tourists.

"Great surveillance and vigilance must be adhered to," said Trump in an additional statement Lewandowski provided to CNN. "We want to be very fair but too many bad things are happening and the percentage of true hatred is too great. People that are looking to destroy our country must be reported and turned in by the good people who love our country and want America to be great again."

Trump confirmed that his policy would not apply to current Muslims in the U.S. during a Fox News interview on Monday evening.

"I have Muslim friends, Greta, and they're wonderful people. But there's a tremendous section and cross-section of Muslims living in our country who have tremendous animosity," he told Fox News anchor Greta Van Susteren. "It does not apply to people living in the country, except we have to be vigilant."

Republicans react

It didn't take long for the rest of the Republican presidential primary field to repudiate Trump's call.

New Jersey Gov. Chris Christie slammed Trump's proposal in a radio interview.

"This is the kind of thing that people say when they have no experience and don't know what they are talking about. We do not need to resort to that type of activity nor should we," Christie said on the Michael Medved radio show. "What we need to do is to increase our intelligence activities. We need to cooperate with peaceful Muslim Americans who want to give us intelligence against those who are radicalized."

And South Carolina Sen. Lindsey Graham called on every presidential candidate to "do the right thing & condemn @Realdonaldtrump's statement."

Graham later told CNN that Trump's rhetoric "is putting our troops serving abroad and our diplomats at risk."

"For interpreters and others risking their lives abroad to help America -- this is a death sentence," Graham said.

Graham just returned from a trip to visit troops in the Middle East and said from troops and allies there expressed concerns over Trump's rhetoric.

Graham said he assured them that Trump is in the minority, but Graham said Monday Trump's latest proposal makes it harder to convince them of that.

Another GOP presidential contender, Texas Sen. Ted Cruz, said, "‎That is not my policy."

"I have introduced legislation in the Senate that would put in place a three year moratorium on refugees coming from countries where ISIS or al Qaeda control a substantial amount of territory. And the reason is that is where the threat is coming from," Cruz said as he was leaving a South Carolina field office.

In a statement, Ohio Gov. John Kasich said, "This is just more of the outrageous divisiveness that characterizes his every breath and another reason why he is entirely unsuited to lead the United States."

And former Florida Gov. Jeb Bush tweeted that Trump is "unhinged."

"Donald Trump is unhinged. His "policy" proposals are not serious," he said.

Former neurosurgeon Ben Carson also said is opposed to placing a religious test on U.S. visitors.

"Everyone visiting our country should register and be monitored during their stay as is done in many countries. I do not and would not advocate being selective on one's religion," he said in a statement.

Kentucky Sen. Rand Paul's campaign did not explicitly refute Trump's proposal.

"Sen. Rand Paul has led on the issue of border security, proposing real solutions. That's why earlier this month he introduced legislation to block visitors and immigrants from nations with known radical elements while a new system is developed to screen properly," said Sergio Gor, Paul's communications director, in a statement.

Former tech CEO Carly Fiorina said Trump's "overreaction" is as bad as Obama's "under reaction."

"President Obama isn't prepared to do anything, which is clearly foolish, but Donald Trump always plays on everyone's worst instincts and fears. And saying we're not going to let a single Muslim into this country is a dangerous overreaction," she said during a gaggle with reporters in Waterloo, Iowa.

Florida Sen. Marco Rubio said he disagrees with Trump.

"(Trump's) habit of making offensive and outlandish statements will not bring Americans together. The next president better be somebody who can unite our country to face the great challenges of the 21st Century," he said in a statement.

Former Virginia Gov. Jim Gilmore tweeted, "Trump's fascist talk drives all minorities from GOP."

And former Vice President Dick Cheney, speaking with conservative radio host Hugh Hewitt, said such a policy goes against the spirit of America.

"This whole notion that somehow we can just say no more Muslims, just ban a whole religion, goes against everything we stand for and believe in," he said. "I mean, religious freedom has been a very important part of our history and where we came from."

Democrats slam Trump

Democrats were quick to condemn Trump's call, with two of the three Democratic presidential candidates calling Trump a "demagogue."

".@realdonaldtrump removes all doubt: he is running for President as a fascist demagogue," tweeted Democratic presidential candidate Martin O'Malley, the former governor of Maryland.

Sen. Bernie Sanders of Vermont also slammed Trump as a demagogue and suggested Trump's rhetoric would make the U.S. weaker.

"Demagogues throughout our history have attempted to divide us based on race, gender, sexual orientation or country of origin. Now, 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," Sanders said in a statement.

Democratic front-runner Hillary Clinton, in a signed message, tweeted, "This is reprehensible, prejudiced and divisive. @RealDonaldTrump, you don't get it. This makes us less safe. -H"

And the Democratic National Committee sought to align the GOP as a whole alongside Trump.

"Donald Trump is indeed a 'net positive' for the Republican Party -- as their chairman called him -- because he shows America what the Republican Party really stands for with his rhetoric that only helps enemies like ISIL/Daesh to recruit extremists," said DNC spokeswoman Christina Freundlich.

Trump's call for a shutdown of Muslim immigration in the U.S. came hours before he was set to speak aboard the U.S.S. Yorktown, a World War II era ship parked near Charleston, South Carolina.