Donald Trump dismissed criticism at home and abroad Tuesday over his "grossly irresponsible" call to bar Muslims from entering the United States, as the White House branded him unfit to lead.

Trump, the leading candidate for the Republican presidential nomination, made the provocative remarks — just his latest on a range of topics on the campaign trail — after last week's shooting that left 14 dead in California by a Muslim couple said to have been radicalised.

In an address Sunday from the Oval Office, President Barack Obama called the attack in San Bernardino an "act of terrorism," but stressed there was no "war between America and Islam."

Less than 24 hours later, Trump triggered calls for him to be barred from taking power after he urged a "total and complete shutdown of Muslims entering the United States until our country's representatives can figure out what is going on."

The bombastic 69-year-old billionaire real estate mogul was unrepentant Tuesday, even as criticism rained down from the White House and as far afield as Ottawa, London and Cairo, where Egypt's official religious body Dar al-Iftaa denounced his "extremist and racist" comments.

Trump stood his ground. Asked by ABC News whether he regretted calling for the ban, he said "Not at all. We have to do the right thing."

And confronted with the charge that extremists would use Trump's rhetoric as a recruiting tool, the candidate scoffed.

"I'm the worst thing that's ever happened to ISIS," he said.

WHITE HOUSE

The strongest reaction came in the United States, where White House spokesman Josh Earnest said Trump's proposals were unconstitutional and challenged the mogul's fellow Republicans to denounce him.

Earnest was scathing and deeply personal, painting Trump — who has never held elected office — as a "carnival barker" with "fake hair."

"What Donald Trump said yesterday disqualifies him from serving as president," concluded Earnest, describing the remarks as "offensive" and "toxic."

Trump, whose comments were extreme even by his populist standards, was similarly lambasted by leading Republicans and campaign rivals.

Trump was the "ISIL man of the year," thundered Senator Lindsey Graham, referring to his belief that Trump was succeeding only in fuelling the radical ideology of the Islamic State group.

"Do you know how you win this war? You side with people in the faith who reject this ideology, which is 99 per cent," Graham told CNN, before invoking Trump's campaign slogan — "make America great again."

"And do you know how you make America great again?" asked Graham, who is lagging badly in the nomination race.

"Tell Donald Trump to go to hell."

Other Republican contenders lined up to reject Trump's proposal.

Hillary Clinton, the Democratic presidential frontrunner, said Trump was playing "right into the hands of terrorists" and Rick Kriseman, a Democratic mayor in Florida, tweeted he was "barring Donald Trump from entering St. Petersburg until we fully understand the dangerous threat posed by all Trumps."

EXTREMISTS

Zeid Ra'ad Al Hussein, the UN High Commissioner for Human Rights, said Trump's comments could "lead to the victimization of the innocent" by extremists.

"It is grossly irresponsible, given the aim of these extremists, to play into their hands at the expense of the vast majority of ordinary Muslims."

Muslim leaders in the United States hit out too.

Sohaib Sultan, Muslim Life Coordinator and Chaplain at Princeton University, drew parallels between Trump and the radical ideology of the Islamic State group.

"ISIS is to Islam what Donald Trump is to American values: a complete distortion of everything that we as a country and a society stand for."

But Sultan also lambasted other Republicans.

"A lot of Republican candidates have really been using similar type of rhetoric throughout the election cycle as well," he told CNN.

Trump showed little inclination to back down, instead comparing the proposed ban to actions taken by Franklin Roosevelt against Japanese and German "enemy aliens" during World War II, though he stopped short of advocating internment camps.

Asked by ABC News whether he was concerned about being increasingly compared to Nazi leader Adolf Hitler, Trump said "No, because what I'm doing is no different than FDR."

Even "Harry Potter" author J.K. Rowling weighed in, saying he was worse than the notorious villain in her blockbuster books.

"How horrible. Voldemort was nowhere near as bad," she tweeted.

The British government was similarly unimpressed.

Prime Minister David Cameron "completely disagrees" with the remarks, which are "divisive, unhelpful and quite simply wrong," a spokeswoman for the Conservative leader said.

Amid the uproar, Trump announced on Twitter that he would travel to Israel by year's end, but that he would not be visiting Jordan at this time, as earlier reported.