LONDON - Presumptive Republican presidential nominee Donald Trump says he may have a poor relationship with British Prime Minister David Cameron in light of his criticism of Trump's call for all Muslims to be temporarily banned from entering the United States.

In an interview broadcast Monday on ITV's Good Morning Britain, Trump also describes London's new mayor, Sadiq Khan, as rude for calling him ignorant.

Cameron has refused to retract comments describing the billionaire candidate's proposed Muslim ban as "divisive, stupid and wrong."

Asked about Cameron's view, Trump says: "It looks like we are not going to have a very good relationship. Who knows, I hope to have a good relationship with him but he's not willing to address the problem either."

Britain's Prime Minister David Cameron leaves Downing Street in London, December 2, 2015. REUTERS

"We have a tremendous problem with radical Islamic terror," Trump told ITV. "The world is blowing up and it's not people from Sweden that's doing the damage, okay? So we have a real problem."

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Trump says he is "not stupid" and denied he was divisive.

Asked by the British interviewer whether he was offended by the comments made by London's first Muslim mayor, Trump said he was.

Soon after Khan won the London mayoral election -- by a large margin -- Trump said the British politician could be an "exception" to the hypothetical ban on Muslims entering the U.S.

"I think Donald Trump has ignorant views about Islam. It's not just about me, I don't want to be the exception to be allowed to go to America," Khan replied. "You can be a Muslim and you can be European... And I hope Donald Trump looks to the lessons that London sent last Thursday (with the mayoral election) and recognizes that it's possible to be Western and Muslim."

It appeared to be the "ignorant" label which most offended Trump. And he hurled it right back -- with what seemed a clear threat to hold a grudge.

"He doesn't know me, never met me, doesn't know what I am all about. I think they are very rude statements. Frankly, tell him I will remember those statements. They are very nasty statements," Trump said. "It is ignorant for him to say that."