It has prompted very strong criticism, including from some of his fellow Republican candidates and state party leaders.
The Philadelphia Daily News cover Tuesday morning labels Trump "The New Furor."
Trump's proposal came the day after President Obama's Sunday night televised address from the Oval Office in which the president urged Americans to reject discrimination against Muslim Americans.
"I wrote something today that I think is very very salient, very important and probably not politically correct, but I don't care," Trump said at a rally on an aircraft carrier-turned-museum in South Carolina.
The statement earned him a standing ovation at an event in which two protesters were led out. Trump called for "a total and complete shutdown of Muslims entering the United States until our country's representatives can figure out what is going on."
He cited polls as evidence of "hatred" of Americans by large segments of the Muslim population. One was a survey from Pew Research. He didn't include specifics, so it's not clear what the data there really show.
A 2011 Pew Global Attitudes survey found majorities of Muslims in other countries described Westerners as "selfish," "violent" and "arrogant."
The Washington Post's Philip Bump pointed out, citing different Pew data:
"The polling firm has found that Muslims across the globe are overwhelmingly opposedto the Islamic State and in 2007 that Muslims were much less likely to view suicide bombings as justified than five years prior. Pew also found a partisan split in which Republican Americans were far more likely to hold negative views of Muslims than Democrats. In 2011, they learned that U.S. Muslims almost never consider suicide bombings to be justified."
At his rally, Trump then went on to highlight another poll.
"This was from the Center for Security Policy, very highly respected group of people, who I know, by the way — 25 percent of those polled agreed violence against Americans is justified. It's Muslims — 25 percent," Trump said.
The poll is highly suspect. Its methodology is questionable — polling online — and its questions in many cases are leading.
There may be a reason for that. While Trump calls the group "highly respected," it's a hawkish, ultra-conservative organization whose website features prominent warnings about the rise of Sharia, or Islamic law, in the U.S. and about the Muslim Brotherhood infiltrating this country.
"The Muslim Brotherhood agenda for the United States demonstrably seeks through subversive infiltration of American institutions the triumph of shariah," the group's president and founder Frank Gaffney writes on the website about a book he endorsed as part of its "Civilization Jihad Reader Series." He continued, "We are now on notice that U.S. Council of Muslim Organizations is simply the leading edge of the jihadist movement in this country. While the USCMO seeks to cloak itself in red, white, and blue, it is only for the purpose of accomplishing what can aptly be described as 'Star Spangled Shariah.' "
Gaffney is known for alleging the infiltration of the Muslim Brotherhood into the U.S., including Grover Norquist of Americans for Tax Reform. Gaffney even has a petition page set up on his group's website seeking to kick Norquist and Suhail Kahn out of the American Conservative Union and accusing them of "running influence operations against conservatives on behalf of the Muslim Brotherhood and other Islamist causes."