"It's about time that somebody spoke up as to radicalism. You have radicalism in this country. It's here. And it's trying to come through," Trump told CNN in an interview.
"I just read where ISIS has gotten ahold of a passport- printing machine for the migrants to get them into the United States. Now, maybe that's true, and maybe it's not. It's an early report.
Trump said his views are not because of polls, but due to his concern on national security.
"I didn't do it for polls, so I don't even care what the polls say. I didn't do it for polls. Now, my polls happen to have gone up a lot since this announcement. A lot of people thought it would go down. I didn't do it for that reason," he said.
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"We have got to stop the problem. There's a real problem. Now, since this, you know, Paris has been very tough on the mosques. They have been very tough on surveillance. All of a sudden, they're becoming tough. But we have got to stop the problem," he said in response to a question.
When asked whether "those friends" supported the ban he called for last week, Trump said: "Not really. I mean, why would they support the ban?"
"But without the ban, you're not going to make the point. You're not going to be able to make the point."
In a statement issued by his campaign, Trump had called for "a total and complete shutdown of Muslims entering the United States until our country's representatives can figure out what is going on", drawing swift condemnation from rivals and the White House.