In a news release from his campaign Monday, Trump "is calling for a total and complete shutdown of Muslims entering the United States until our country's representatives can figure out what is going on."
Trump cited a report from the Center for Security Policy -- a non-profit organization with conservative ties -- that found about a quarter of Muslims living in the U.S. polled believe that it's "legitimate to use violence to punish those who give offense to Islam by, for example, portraying the prophet Mohammed."
Trump's campaign said the proposal comes in response to the level of hatred among "large segments of the Muslim population" toward Americans.
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.
New York City Mayor Bill de Blasio criticized Trump's call for banning Muslims and recent remarks to a Jewish group for allegedly fostering harmful stereotypes.
During an interview on CNN, he also ripped the Republican presidential candidate's plan to list the nation's Muslims in a database.
The Democrat said Trump's rhetoric was "dangerous" and "doing the bidding of our enemies."
Trump hit back on Twitter, saying de Blasio was "the worst mayor in the United States." Trump says he has watched New York, where he has a home, suffer from dirty streets, homelessness and crime.
N.Y.C. has the worst Mayor in the United States. I hate watching what is happening with the dirty streets, the homeless and crime! Disgrace— Donald J. Trump (@realDonaldTrump) December 7, 2015
He called the state of the city a "disgrace."
Ibrahim Hooper, spokesman for the Council on American-Islamic Relations, spoke to ABC News regarding the announcement.
"It's really incredible that the leading Republican party presidential candidate would make what amounts to almost a fascist statement seeking to bar all Muslims from the United States," he said. "It would have been beyond belief sometime back, but now it seems to be routine in terms of Donald Trump trying to one up himself with his Islamophobic rhetoric. How exactly is he going to accomplish this? Will people be questioned about their faith at the borders? ... It's into an Orwellian, fascist mindset that is just unbelievable."
In a radio interview with Michael Medved, New Jersey Governor Chris Christie strongly repudiated Trump's suggestion, calling it "ridiculous" and "the kind of thing that people say when they have no experience and don't know what they're talking about."
Jeb Bush also chimed in.
Donald Trump is unhinged. His "policy" proposals are not serious.— Jeb Bush (@JebBush) December 7, 2015
Former Vice President Dick Cheney spoke with radio host Hugh Hewitt Monday evening and said, "I think this whole notion that we can just say no more Muslims, and just ban a whole religion goes against everything we stand for and believe in. Religious freedom has been a very important part of our history and where we came from. ... It's a mistaken notion."
Meantime, Deputy National Security Advisor Ben Rhodes called Trump's suggestion "totally contrary" to America's values and security.
"We have in our bill of rights respect for the freedom of religion," he said. "Muslim Americans have made extraordinary contributions to our country, but it's also contrary to our security...The fact of the matter is ISIL wants to frame this as a war between the United States and Islam. And if we look like we're applying religious tests who comes into this country, we're sending a message that essentially we're embracing that frame. And that is going to make it very difficult to partner with Muslim communities here in the United States and around the world to prevent this scourge of radicalization that we need to be focused on. We should be making it harder for ISIL to portray this as a war between the United States and Islam, not easier."
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(Some information from the Associated Press)