US President Barack Obama said Tuesday that Republican presidential nominee Donald Trump is "unfit" to be president and "he keeps on proving it."

At a White House news conference, Obama questioned why party leaders continue backing Trump even after their repeated denunciations of his statements.

The president was asked about the Republican nominee's recent comments about the parents of Humayun Khan, a US Army captain who died defending his base from a car bomber in 2004 in Iraq.

Trump sparked an uproar when he attacked the family after Khan's father, Khizr Khan, criticized him in a speech to the Democratic National Convention, suggesting Trump had never read the US Constitution and had never made any sacrifices for his country.

Obama said Trump's attacks on the Khans and "the fact that he doesn't appear to have basic knowledge around critical issues in Europe, in the Middle East, in Asia, [mean] that he's woefully unprepared to do this job."

Obama said it was significant that his opinion of the candidate's character and competence is shared by many prominent Republicans, and asked why leaders of the conservative party are still supporting Trump after it has become clear that such statements are not just occasional gaffes.

Republican leaders should recognize that somebody who makes those kinds of statements "doesn't have the judgement, the temperament, the understanding, to occupy the most powerful position in the world," Obama said.

Trump responded with a statement blaming Obama and Democratic presidential nominee Hillary Clinton for a litany of problems the US has domestically and internationally.

"Obama-Clinton have single-handedly destabilized the Middle East, handed Iraq, Libya and Syria to [the Islamic State movement], and allowed our personnel to be slaughtered at Benghazi," Trump said.

He statement accuse them of allowing US veterans to be mistreated, releasing "criminal aliens" who have killed innocent Americans and shipping jobs overseas "to appease their global special interests."

He said Clinton "put the whole country at risk with her illegal email server, deleted evidence of her crime, and lied repeatedly about her conduct, which endangered us all."

Trump earlier labelled Clinton "the devil" and suggested the November elections could be rigged. Bernie Sanders, the Vermont senator and once Clinton's rival for the nomination, is also "the devil," according to Trump.

At a campaign rally Monday he slammed Sanders for endorsing Clinton: "He made a deal with the devil. She's the devil."

At another rally he said: "I'm afraid the election is going to be rigged," without offering any evidence or explanation for his allegations.

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