The state should back institutions such as schools, courthouses and immigration centres which require individuals to remove face-coverings such as the niqab veil worn by some Muslim women, Prime Minister David Cameron said.
Mr Cameron said he did not believe there should be a ban on wearing the niqab - which conceals the whole face - in the streets.
But he made clear he was "happy" to look at the issue of whether the state needed to do more to back up institutions which choose to implement a ban.
Mr Cameron told BBC1's Andrew Marr Show: "We are a free country and people should be free to wear whatever clothes they like in public or in private.
"But we should support those institutions that need to put in place rules so that those institutions can work properly.
"So for instance in a school, if they want that particular dress code, I believe the Government should back them. The same for courts, the same for immigration.
"I think we should back those institutions that want to have sensible policies that actually have a particular purpose."
Asked if he would respond to a judge's suggestion that there should be national guidelines on the wearing of the niqab in court, Mr Cameron said: "I'm very happy to look at that.
"Obviously, in court the jury needs to be able to look at someone's face. I've sat on a jury, that's part of what you do.
"When someone is coming into the country, an immigration officer needs to see someone's face.
"In a school, it's very difficult to teach unless you can look at your pupils in the eye.
"It's a free country and I think a free country should have free and independent institutions. No plans for anything on the street, but if the Government needs to do more to back up institutions, then I would be happy to look at that."