"You have radicals that are doing things. I mean, it wasn't people from Sweden that blew up the World Trade Center, Jake," Trump told CNN's Jake Tapper on "State of the Union."

His comments come after a controversy that erupted late last week when, at a Trump campaign event, a man said, "We have a problem in this country -- it's called Muslims."

He defended his decision not to correct the man, saying, "It was a question that was asked in front of a totally packed house."

Trump also said he has friends who are Muslims -- but that the religion's extreme elements are responsible for terrorist attacks.

"We do have a problem with radical Muslims, there's no question about that," Trump said Sunday.

Trump also wouldn't say whether he believes -- as the man at his campaign event falsely claimed -- that President Barack Obama is a Muslim who wasn't born in the United States. Obama is a Christian who was born in Hawaii.

Asked on NBC's "Meet the Press" whether he'd be comfortable with a Muslim president, Trump said: "Would I be comfortable? I don't know if we have to address it right now. But I think it is certainly something that could happen. Some people have said it already happened, frankly -- but of course you won't agree with that" -- a reference to Obama.

"I don't 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 Rev. Wright. And so, you know, I'm willing to take him at his word for that. I have no problem with that," Trump said.

He deflected questions about Obama's place of birth and religion on ABC's "This Week," too.

"Well, you know, I don't get into it, George. I think about jobs. I'm talking about the military. I don't get into it," he said, when asked by host George Stephanopoulos whether he now believes Obama was born in the United States. "Frankly, it's of no longer (of) interest to me. We're beyond that. And it's just something I don't talk about."

Asked about whether Obama isn't a Muslim, Trump said, "George, you have raised the question. I haven't raised the question. I don't talk about it and I don't like talking about somebody else's faith. He talks about his faith and he can do that. But I don't talk about other people's faith. It's not appropriate for me to talk about somebody else's faith."

Four years ago, Trump had pressed Obama to release his birth certificate -- which Obama did.