British Prime Minister David Cameron has refused to retract comments describing US presidential candidate Donald Trump's proposed Muslim ban as "divisive, stupid and wrong".

Cameron is, however, "committed to maintaining special relationship" with the United States no matter who wins the presidential election, his spokesman, Dan York-Smith, said on Monday.

"He has been clear that he will work with whoever is president of the United States," York-Smith said.

Cameron's latest comment came in response to Trump's interview with ITV's "Good Morning Britain", broadcast on Monday. 

"It looks like we are not going to have a very good relationship," Trump said in the interview conducted in New York.

"Who knows, I hope to have a good relationship with him [Cameron] but he's not willing to address the problem either."

In the interview conducted on Saturday, Trump also described London's new mayor, Sadiq Khan, as "rude" for calling him ignorant.

The property tycoon said that he would "remember" the mayor's hostile reaction to the idea that Khan, a Muslim, would be given an exception to the temporary ban.

'Rude statements'

"He doesn't know me, hasn't met me, doesn't know what I'm all about. I think they were very rude statements and, frankly, tell him I will remember those statements," Trump said. "They are very nasty statements."

Trump denied that he was "at war" with Khan.

"I just think it's very rude of him. In fact it's the opposite," he said. "I wished him well when I heard he won, he's a Muslim, I think it's ignorant for him to say that."

Khan's office said American voters would reject Trump's views.

"Sadiq has spent his whole life fighting extremism, but Trump's remarks make that fight much harder for us all - it plays straight into the extremists' hands and makes both our countries less safe," his office said in a statement.

When reminded that Khan has described Trump as ignorant, Trump shook his head and said: "Let's do an IQ test."

The mayor's office rejected the idea, saying "ignorance is not the same thing as lack of intelligence".

Source: Agencies