Washington, United States: Republican presidential frontrunner Donald Trump called Monday for a "total and complete shutdown" of Muslims entering the United States, following last week's mass shooting in California by a Muslim couple believed to have been radicalized.

A statement from Trump's campaign team said the halt on Muslims entering the country should remain in place "until our country's representatives can figure out what is going on."

Trump's aides did not specify if the proposal would affect both tourists and immigrants, and also did not say if it would target American Muslims currently abroad.

The statement drew sweeping condemnation by presidential rivals and the White House, which denounced Trump's call to bar Muslims as "totally contrary" to US values.

"We have, in our Bill of Rights, respect for the freedom of religion," one of President Barack Obama's top foreign policy aides, Ben Rhodes, told CNN.

Trump's campaign cites poll data allegedly showing "hatred toward Americans by large segments of the Muslim population."

"Where this hatred comes from and why we will have to determine," the billionaire real estate mogul, who is leading in opinion polls among likely Republican voters, said in the 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 has been increasingly virulent in his remarks targeting Muslim Americans since the deadly Paris attacks, and again in the wake of last week's shooting rampage in California, which left 14 dead and 21 wounded.

Last month, he caused a furor when he claimed he saw "thousands and thousands of people" cheering in parts of New Jersey with substantial Arab-American populations as the Twin Towers collapsed on September 11, 2001.

But his latest statement was particularly jarring.

"Just put out a very important policy statement on the extraordinary influx of hatred & danger coming into our country. We must be vigilant!" Trump tweeted after the statement was released.

His announcement unleashed severe condemnation on Twitter, including from other Republicans running for president.

"Donald Trump is unhinged," former Florida governor Jeb Bush tweeted. "His 'policy' proposals are not serious."

"Every candidate for president needs to do the right thing & condemn@realDonaldTrump's statement," Senator Lindsey Graham added.

Democratic presidential contender Martin O'Malley said Trump's incendiary comment "removes all doubt: he is running for president as a fascist demagogue."