Donald Trump has reportedly suggested new London mayor Sadiq Khan would be exempt from his proposed ban on Muslims entering the US.
It comes after Khan said any visit to see counterparts in New York and Chicago would have to be made before the presidential inauguration in January in case Trump makes it to the White House.
The billionaire sparked international condemnation when he proposed a temporary ban on Muslims entering the US after the Paris terror attacks.
David Cameron labelled the idea "stupid" and calls to ban Trump from entering Britain were raised in Parliament after a petition attracted nearly 600,000 signatures.
Asked by the New York Times how the ban would affect the new London mayor, Trump said there would "always be exceptions".
The presumptive Republican candidate said he was "happy" voters had chosen Khan, a practising Muslim, adding that it would be a "very good thing" if he is successful in the role.
Around the time of his comments on banning Muslims from the US, Trump provoked further criticism by claiming parts of London were "no-go areas" as some areas of the capital were "so radicalised that the police are afraid for their own lives".
After being declared winner of the mayoral race on Saturday, Khan said he rejected the "politics of fear" as he promised to be a "mayor for all Londoners".
Commenting on the election, Trump said: "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."
Asked to explain, he added: "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 is considered a shoo-in for the Republican presidential candidacy after the withdrawal of his only remaining rival, John Kasich, last week, leaving an election battle against Democrat Hillary Clinton likely.
Khan told Time magazine he was confident Trump's approach to politics would not prevail when America goes to the polls in November.
He warned: "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."