Presidential hopeful Donald Trump has said the newly elected mayor of London would be an "exception" to his proposed ban on Muslims travelling to the US.

Because of his faith, Sadiq Khan had expressed concern that he would not be able to visit the US if Trump were elected.

Trump proposed a ban on Muslims entering the US after attacks in Paris killed 130 people last year.

"There will always be exceptions," the Republican businessman said.

READ MORE: Trump urges US ban on Muslim arrivals

The temporary ban has been widely criticised in the US and abroad but Trump has stood by the proposal, saying it is needed to ensure US security.

Trump said he was "happy" that Khan would be leading London.

"If he does a good job and frankly if he does a great job, that would be a terrific thing," he added.

Khan - the son of Pakistani immigrants - is London's first Muslim mayor, after beating Conservative rival Zac Goldsmith for the Labour Party by 1,310,143 votes to 994,614.

"I want to go to America to meet with and engage with American mayors," Khan told Time magazine. "If Donald Trump becomes the president I'll be stopped from going there by virtue of my faith."

He added that he was "confident that Donald Trump's approach to politics" would not prevail in America.