Republican presidential hopeful Donald Trump has said it is “not his job” to defend President Barack Obama, after criticism from fellow Republicans for not correcting a supporter who said the POTUS was a Muslim.

Donald Trump tweeted there was “no chance” Barack Obama would defend him if he was similarly attacked.

South Carolina Senator Lindsey Graham has said Donald Trump should apologize.

Donald Trump canceled his appearance at a big Republican event on September 18.

The tycoon’s campaign team said he had pulled out of the Heritage Foundation because of a “significant business transaction” that needed his attention.

The criticism has been piling up since a man at Donald Trump’s rally in New Hampshire on September 17 prefaced a question by saying Barack Obama was a Muslim and “not even an American”.

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The supporter went on to say: “We have a problem in this country – it’s called Muslims.”

Donald Trump let it go unchallenged and within a few hours, Democratic frontrunner Hillary Clinton said his failure to denounce “hateful rhetoric” was “disturbing and wrong”.

On September 18, his Republican competitors for the nomination waded into the row.

“He’s playing into this hateful narrative and he has to set it right,” said Lindsey Graham, who said he would never question the president’s faith or patriotism.

Leaders have an “obligation” to correct such statements, said another Republican presidential hopeful, New Jersey Governor Chris Christie.

Donald Trump hit back in a series of tweets: “Am I morally obligated to defend the president every time somebody says something bad or controversial about him? I don’t think so!

“If someone made a nasty or controversial statement about me to the president, do you really think he would come to my rescue? No chance!”

Donald Trump added that if he had challenged the man he would have been accused of interfering with his right to free speech.

Barack Obama, who has spoken openly about his Christian faith, was born to an American mother and Kenyan father in Hawaii.

In 2011, Donald Trump challenged Barack Obama to produce his birth certificate to disprove rumors that he was born in Kenya, which the president did.