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Donald Trump today launched an astonishing fresh attack on "nasty" Sadiq Khan and admitted he may not have a "good relationship" with David Cameron after he vowed to ban Muslims from the US.

The billionaire Republican hit back after London's first Muslim mayor warned his "ignorant" views on religion will make the world less safe if he becomes President.

David Cameron also said Mr Trump's plan for a temporary border ban was "stupid, divisive and wrong".

Yet in an interview with Piers Morgan, Mr Trump said he was offended by Mr Khan's "ignorant" remarks and even challenged him to an IQ test.

"He doesn't know me, hasn't met me, doesn't know what I'm on about," he told ITV's Good Morning Britain host.

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"I think they're very rude statements and frankly tell him I will remember those statements. They're very nasty statements.

"I think it's ignorant for him to say that."

He added: "We have a tremendous problem with radical Islamic terror. Look at it worldwide. The world is blowing up and it's not people from Sweden that's doing the damage, OK?"

A spokesman for the London mayor hit back within hours, saying: "Donald Trump's views are ignorant, divisive and dangerous - it's the politics of fear at its worst and will be rejected at the ballot box just as it was in London.

(Image: Jack Taylor/Getty Images)

"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."

He said there were "no plans" to seek direct talks and mocked Mr Trump's challenge to the mayor to take an IQ test.

"Ignorance is not the same thing as lack of intelligence," he added.

Mr Trump signalled he was backing down over the ban on Muslims today, saying: "I'm not the President. Everything's a suggestion".

But he admitted the Special Relationship could suffer if he beats Democrat frontrunner Hillary Clinton to the White House in November.

On David Cameron, he said: "It looks like we're not going to have a very good relationship.

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

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(Image: Getty Images)

The Tory PM said last year that if Trump came to Britain, he would unite the country against him.

Yet despite the offence he caused Mr Trump said: "I don't think I'm a divisive person. I'm a unifier."

When asked about Britain's membership of the EU, he added: "I've dealt with the European Union, it's very very bureaucratic, it's very very difficult.

"In terms of Britain I would say 'what do you need it for'?

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"But again, let people make up their own mind."

On being elected as London Mayor, Mr Khan said Mr Trump was "ignorant" in his views on Islam and he risked harming security on both sides of the Atlantic.

Mr Trump said: "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.

(Image: Rob Stothard)

"They are very nasty statements."

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He added: "When he won I wished him well. Now, I don't care about him, I mean it doesn't mean any difference to me, let's see how he does, let's see if he's a good mayor."

Asked if he was offended by Mr Khan's public denouncement he replied: "Yeah, I am."