WASHINGTON — Amid fear of terrorism, the Republican candidates for president for months have escalated their rhetoric about the place of Muslims in the United States.

A Muslim shouldn’t be president. Muslims fleeing war-torn Syria and Iraq should be barred from the country. Mosques should be placed under surveillance and shut down if people are radicalized in them.

Republican front-runner Donald Trump’s call Monday for a “total and complete shutdown of Muslims entering the United States” was the latest salvo for a party aggressively testing the boundaries between concerns about security and discrimination against a religious group.

For most of Trump’s rivals in the 2016 race, as well as numerous other Republicans, it was also the proposal that finally crossed that line.

“Donald Trump is unhinged,” former Florida Gov. Jeb Bush said via Twitter. “His ‘policy’ proposals are not serious.”

South Carolina Republican Chairman Matt Moore, whose state is third on the primary voting calendar, said that “as a conservative who truly cares about religious liberty, Donald Trump’s bad idea and rhetoric send a shiver down my spine.”

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.

Trump has faced pushback from within his party for earlier comments about Muslims, but never with such speed and force.

Some rivals challenged his debunked assertion that thousands of Muslims living in New Jersey cheered the 9-11 attacks.

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 Texas Sen. Ted Cruz. If the real estate mogul’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. Following the Nov. 13 attacks in Paris, the fear of Islamic State-inspired attacks drew even closer last week when a married couple killed 14 people in San Bernardino, Calif. The FBI said both had been radicalized for some time and the woman claimed allegiance to the Islamic State on Facebook shortly before the attack.