Updated at 7:43 p.m.
"Without looking at the various polling data, it is obvious to anybody the hatred is beyond comprehension," Trump is quoted as saying in the statement. "Where this hatred comes from and why we will have to determine. 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."
At a rally in Mount Pleasant, South Carolina on Monday evening, Trump pointed to the statement he released earlier in the day.
“Should I read you the statement?” he asked.
The crowd enthusiastically agreed that he should.
“Donald J. Trump is calling for a total and complete shutdown of Muslims entering the United States until our country's representatives can figure out what the hell is going on,” he said, adding the word “hell" for emphasis this time.
Supporters erupted in applause.
“We have no choice. We have no choice,” Trump said. "We have no choice.”
Earlier in the rally, which was interrupted by protests, Trump said, "I have friends that are Muslims. They are great people -- but they know we have a problem."
Trump campaign manager Corey Lewandowski told the Associated Press that the ban would apply to "everybody," including both immigrants and tourists. Soon after the statement was released, Trump tweeted that he had "just put out a very important policy statement on the extraordinary influx of hatred and danger coming into our country." He added in the tweet: "We must be vigilant!"
In an interview on Fox News Channel shortly ahead of his campaign rally, Trump was asked whether his policy would apply to Muslim military personnel stationed overseas who want to come home.
"They will come home. We have to be vigilant," he responded. "We have to take care of the Muslims that are living here. But we have to be vigilant."
He later added: "Anybody here stays, but we have to be very vigilant... This does not apply to people living in the country except that we have to be vigilant."
In the past month, particularly following the recent mass shooting in Southern California that is believed to have been inspired by the Islamic State terrorist group, Trump has called for greater scrutiny of Muslims -- including Muslim Americans who are legal residents of the country. He has said he would support heavy surveillance of mosques, bar Syrian refugees of all religions from entering the country and would consider establishing a database to track all Muslims in the country. But Trump's statement on Monday was his most controversial proposal yet.
Trump typically announces major positions like this in media interviews or at rallies, rarely issuing formal statements. The statement immediately sparked rounds of questions about how such a policy would work, along with strong criticism.
"Oh, my goodness," said Ibrahim Hooper, national communications director at the Council on American-Islamic Relations. "One has to wonder what Donald Trump will say next as he ramps up his anti-Muslim bigotry. Where is there left for him to go? Are we talking internment camps? Are we talking the final solution to the Muslim question? I feel like I'm back in the 1930s."
What worried Hooper, he said, was the premeditated nature of Trump's statement.
"He feels perfectly okay saying this," said Hooper. "It's not an open mic moment, where he has to walk something back. This was a statement from his campaign. They had to believe that this would be well received by his supporters. We've always had anti-Muslim bigots, but they've always been at the fringes of society. Now they want to lead it. In saner times, his campaign would be over. In insane times, his campaign can gain support. And that's why he put it out."
David Weigel and Sean Sullivan contributed to this report.