Republican presidential candidate Donald Trump dismissed critics who have accused him of failing to stand up for Muslim Americans after a controversial town hall exchange last week, repeatedly stating during a media blitz on Sunday that he has Muslim friends who are “amazing people.”

“I have friends that are Muslims. They are great people, they are amazing people…but we certainly do have a problem. I mean, you have a problem throughout the world,” Trump said on CNN’s “State of the Union."

“You have radicals that are doing things. I mean, it wasn’t people from Sweden that blew up the World Trade Center, Jake,” he told host Jake Tapper.

Trump’s comments come amid a days-long controversy stemming from a town hall event in New Hampshire on Thursday. At the event, a questioner told him that “we have a problem in this country. It’s called Muslims.” The man also accused President Obama of lying about being born in the United States and about his Christian faith.

[What the media gets wrong about Donald Trump’s Obama-Muslim flap]

Trump, who has been one of the most prominent voices in the “birther” movement, did not directly respond to the question and did not indicate displeasure with that characterization of Muslims. His critics have since pounced, saying that his decision not to push back on those comments is consistent with a broader tendency toward anti-immigrant rhetoric.

“Most [Muslims] are fabulous. And I have friends that are Muslims,” Trump told George Stephanopoulos on ABC’s “This Week.” “… But there is a problem with militancy, and it is something that is going to have to be solved."

Trump, during an interview on NBC’s “Meet the Press,” would not say whether he would support a Muslim for president, saying, “I don't know if we have to address it right now.”

“I think it is certainly something that could happen,” he said. “I mean, some people have said it already happened, frankly. But of course you wouldn't agree with that.”

When pressed by host Chuck Todd on whether he believes Obama is a Christian, Trump told him that he is not responding to those questions because he does not talk about people’s faith.

“Now, in all fairness, he said he was a Christian and he said he is a Christian. He attended the church of Reverend Wright. And so, you know, I'm willing to take him at his word for that. I have no problem with that,” Trump said.

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