Justice secretary Robert Buckland has said the wearing of face coverings in public places such as shops should “perhaps” be made mandatory.
It comes after Cabinet Office minister Michael Gove yesterday said face coverings should not be made mandatory.
Boris Johnson said on Friday the government could introduce “stricter” rules on where coverings have to be worn.
But the prime minister stopped short of setting out what any new requirements might be.
At present, in England, face coverings are compulsory on public transport but not shops.
In Scotland, a law making face coverings in stores mandatory for most people came into effect on Friday.
Asked on BBC Radio 4’s Today programme on Monday whether he is in the “mandatory perhaps” or “mandatory never” camp, Buckland said: “I think I’m ‘mandatory perhaps’.
“Wearing them in an enclosed space where you’ve got lots of people, for example a busy shop, seems to be sensible.
“It is all about increasing confidence. I think the more of us who do the courteous and responsible thing, the more people you’ll see venture out into shops.”
He added: “If it becomes necessary to nudge people further by taking further action then of course we will consider that. I think the matter is under careful and daily review.”
Asked by the BBC’s Andrew Marr Show on Sunday if face coverings should be mandatory in shops, Gove said: “I don’t think mandatory, no.”
The senior minister said wearing a covering was “basic good manners” and that he had “trust” in “people’s good sense”.
Johnson said the shift in messaging towards advocating the wearing of face coverings had come as “balance of scientific opinion seems to have shifted more in favour of them”.
The mix messaging over face coverings comes as beauty salons, nail bars and tattoo shops are to open for the first time in four months as part of the latest relaxation of lockdown restrictions in England.
Spas, massage studios and physical therapy businesses will also be able to welcome customers again from today.