New London mayor Sadiq Khan has hit out at Donald Trump's "ignorant" view of Islam after the US presidential hopeful suggested he would exempt him from his proposed ban on Muslims entering America.

Mr Trump, who is widely expected to be confirmed as the Republican candidate for the presidency, appeared to extend an olive branch to Mr Khan when he welcomed his election as the first Muslim mayor of a major European capital.

Asked by the New York Times how his proposed ban on Muslims would apply to Mr Khan, Mr Trump said: "There will always be exceptions."

But the offer was brusquely brushed aside by Mr Khan who warned that the billionaire businessman's outspoken views on Islam risked endangering people on both sides of the Atlantic.

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

"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," he said.

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

Earlier Mr Khan had warned that if he wanted to meet his counterparts in New York and Chicago, he would have to go before the presidential inauguration in January in case Mr Trump succeeded in gaining the White House.

"I want to go to America to meet with and engage with American mayors.

"If Donald Trump becomes the president I'll be stopped from going there by virtue of my faith, which means I can't engage with American mayors and swap ideas," he told Time magazine.

However Mr Trump, who has been seeking to soften his image since all but clinching the Republican nomination, insisted that he welcomed Mr Khan's election.

"I was happy to see that. 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," he said.

"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."

During the mayoral election Mr Khan repeatedly attacked his Conservative rival Zac Goldsmith for adopting Trump-like tactics, accusing him of running a campaign based on fear and division.