Donald Trump's view of Islam is "ignorant" and could make both the US and the UK less safe, according to the Mayor of London, Sadiq Khan.

Khan is the city's first Muslim mayor and rejected the US presidential candidate's offer that he could be an "exception" to Trump's proposed policy of a "total and complete shutdown of Muslims entering the United States".

"This isn't just about me – it's about my friends, my family and everyone who comes from a background similar to mine, anywhere in the world," said Khan.

"Donald Trump's ignorant view of Islam could make both our countries less safe – it risks alienating mainstream Muslims around the world and plays into the hands of the extremists.

"Donald Trump and those around him think that western liberal values are incompatible with mainstream Islam – London has proved him wrong."

Khan's rebuff came after Trump told the New York Times on Monday that he was happy to see Khan elected and that "there will always be exceptions" to his suggested temporary ban on Muslims.

He said of Khan's election: "I think it's a very good thing, and I hope he does a very good job because frankly that would be very, very good. Because I think if he does a great job, it will really — you lead by example, always lead by example. If he does a good job and frankly if he does a great job, that would be a terrific thing."

Trump announced his controversial policy in the aftermath of the terrorist attacks in San Bernadino when 14 people were killed in shooting inspired by ISIS.

The New York billionaire has stuck by his ban despite outrage from world leaders. Prime Minister David Cameron labeled Trump "divisive, stupid and wrong" – a comment he has declined to apologise for since Trump's rise to become the Republican presumptive nominee.