US presidential hopeful Donald Trump has promised to exempt London’s first Muslim mayor Sadiq Khan from his ban on Muslims travelling to the United States if he wins the White House, in an interview to a US newspaper.

Donald Trump vowed to temporarily shut down the US border for Muslims after last December’s lethal attack in San Bernardino by a radicalized couple with links to Islamists.

"There will always be exceptions," the presumptive Republican nominee told the New York Times on Monday when he was asked if the ban would affect Khan.

This came after Khan, a UK national of Pakistani descent, told Time magazine he feared that he would not be able to travel to the United States by virtue of his faith.

Earlier this month, the Labour candidate won the London mayoral election against Conservative contender Zac Goldsmith, becoming the first Muslim to take the UK capital's top job.