After doubling down on his proposal to ban some immigrants by including those from countries with a history of terrorism, Donald Trump is now doubling down on another controversial idea in the wake of the Orlando massacre: profiling Muslims already in the United States.

In an interview with CBS's John Dickerson that aired Sunday on "Face the Nation," Trump called profiling Muslims "common sense."

"Well, I think profiling is something that we're going to have to start thinking about as a country," he said when Dickerson asked Trump whether he still supports the idea, which he has floated before. "And other countries do it; you look at Israel and you look at others and they do it and they do it successfully. You know, I hate the concept of profiling. But we have to start using common sense, and we have to use, you know, we have to use our heads ... we really have to look at profiling. We have to look at it seriously."

Trump's endorsement of broad profiling of Muslims in the United States appears to take him closer yet to supporting a radical shift in U.S. counterterrorism policy. In the wake of the San Bernardino, Calif., shooting in December, he expressed support for limited profiling of Muslims — if neighbors or relatives seemed suspicious.

"Well, I think there can be profiling," he told Dickerson at the time. "If they thought there was something wrong with that group and they saw what was happening, and they didn't want to call the police because they didn't want to be profiling, I think that's pretty bad."

In the interview that aired Sunday, Trump appeared to suggest that ethnic profiling could be useful at his political rallies to keep people safe:

"People that obviously had no guns, no weapons, didn't know anything and they were going through screening and they were going through the same, the same, you know, scrutiny. The absolute same scrutiny as somebody else that looked like it could have been a possible person. So we really have to look at profiling."

Ethnic profiling isn't the only controversial policy that Trump has discussed since an American-born man killed 49 at a gay Orlando nightclub.  In a speech the day after the June 12 massacre, he blamed American Muslims for harboring terrorists and proposed temporarily banning any immigrants from countries with a history of terrorism, an apparent refinement of his earlier proposal to temporarily ban   Muslims from entering the country.

And before he clinched the nomination, Trump expressed support for watching U.S. mosques. On Sunday, he told Dickerson it could be done "respectfully" and indicated  he'd look to cities that are closing down mosques as examples.

After he won enough delegates to be Republicans' de facto presidential nominee in May, Trump appeared to back off his more controversial counterterrorism proposals, such as the temporary ban on Muslims entering the United States. His bringing up the idea again after the Orlando massacre earned him criticism from fellow Republicans, including House Speaker Paul D. Ryan (Wis.).