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However, he said people will be legally required to wear face coverings on public transport, in public indoor spaces and in health and care settings beyond that point.
Mr Drakeford confirmed that the Welsh Government will review the requirement every three weeks and lift it as soon as the public health situation allows.
His comments echoed those of Scottish First Minister Nicola Sturgeon who said the use of face coverings in Scotland will remain mandatory “for as long as necessary”.
However, in England, the legal requirement to wear a face covering in shops, public transport and other enclosed spaces will end on July 19.
The UK Government has said it “expects and recommends” that face coverings will be worn in crowded and enclosed spaces.
On Thursday, Mr Drakeford told Good Morning Britain there was “no ambiguity” for people in Wales on the issue of face coverings.
He said it was a way for people in the country to keep each other safe, as well as reassure those classed as clinically vulnerable.
“It’s not simply good advice, it’s what every one of us will be required to do,” Mr Drakeford told the programme.
Asked about the situation in England, Mr Drakeford replied: “I think it will be difficult for people in England to know exactly what is required of them.
“I’ve often been told by the UK Government that we should work to have a four-nation approach to coronavirus and I don’t disagree with that at all.
“But on this issue, the mask-wearing issue, we should be clear.
“It is the UK Government that is the outlier and if they were prepared to bring themselves into line with the decisions that have been made in Scotland and in Wales, for example, that would be clearer and simpler for everybody.”
On Wednesday, Mr Drakeford confirmed that Wales will move fully into Alert Level 1 from July 17, following a four-week pause due to the rise of the Delta variant.
It means up to six people can meet indoors in private homes and holiday accommodation, organised indoor events can take place for up to 1,000 people who are seated and ice rinks can reopen.
If infection numbers remain stable and vaccination rates continue to rise, Wales will move to Alert Level 0 on August 7.
Under this level, nightclubs would be allowed to reopen and limits on the number of people who can meet indoors would be lifted and replaced with a requirement for workplaces to carry out Covid-19 risk assessments.
The incidence rate of Covid-19 in Wales is 145 cases per 100,000 people, the lowest in the UK.
Wales also has one of the highest vaccination rates in the world, with 73% of adults having received both doses.