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President Barack Obama attacked Republican presidential hopeful Donald Trump on Tuesday, saying he was "unfit" to lead the US and called on members of his party to disown him.

Standing alongside the prime minister of Singapore, Obama cast aside any pretense of domestic unity and described Trump as "woefully unprepared" and "unfit to serve as president".

"He keeps proving it. This isn't a situation where you have an episodic gaffe," Obama said.

It comes as the 70-year-old mogul was embroiled in multiple controversies over his comments about Muslims, babies, firefighters and the military.

The president turned the heat up on Republican leaders who have backed Trump, but continued to denounce some of his comments.

"This is daily and weekly where they are distancing themselves from statements he's making," Obama said.

"There has to be a point in which you say: 'This is not somebody I can support for president of the United States, even if he purports to be a member of my party.'"

The attack by Obama, who has endorsed Hillary Clinton in the 2016 White House race, is a significant escalation of presidential rhetoric.

There has to come a point in which you say 'enough'. - President Barack Obama

"There have been Republican presidents with whom I've disagreed with, but I didn't have a doubt that they could function as president," Obama said.

Turning to his 2012 and 2008 election opponents, Obama said "Mitt Romney and John McCain were wrong on certain policy issues, but I never thought that they couldn't do the job."

Obama's comments came amid a roiling war of words between Trump and the father of a slain US soldier who rebuked the Republican nominee as having "sacrificed nothing".

Trump also has come under fire for remarks in a television interview in which he appeared not to be aware of Russia's 2014 annexation of Crimea, after its takeover from Ukraine.

Obama said: "The notion that he would attack a Gold Star family that made extraordinary sacrifices on behalf of our country, the fact that he doesn't appear to have basic knowledge around critical issues in Europe, in the Middle East, in Asia means that he's woefully unprepared to do this job."

"There has to come a point in which you say 'enough'," he said, in a comment directed at Republicans.

Should the American people choose Trump, there will be consequences, because a US election is a global election. - President Francois Hollande

"The alternative is the entire party and the Republican party effectively endorses and validates the positions being articulated by Mr. Trump. As I said in my speech last week, I don't think that represents the views of a whole lot of Republicans out there."

Obama last week addressed the Democratic Party convention in Philadelphia and painted the election not just as a choice between a Democrat and Republican, but a Democrat and a "demagogue" who threatens democracy in the US.

Trump responded in a statement saying that it was Hillary Clinton who was unfit for office as she has embraced policies that have hurt national security and US' workers.

"Hillary Clinton has proven herself unfit to serve in any government office," said the statement.

Abroad, the French President Francois Hollande on Tuesday described Trump's "excesses" as sickening.

"His excesses make you want to retch, even in the United States, especially when - as was Donald Trump's case - he speaks ill of a soldier, of the memory of a soldier," Hollande told journalists in Paris.

"Should the American people choose Trump, there will be consequences, because a US election is a global election," he added.