Considering lockdown restrictions will be the "primary focus" of the Welsh Government this week, the First Minister has told a daily Covid-19 briefing.
Mr Drakeford said he believed a "four nation approach" to easing lockdown would work best.
"Across the United Kingdom, we entered lockdown on the same day and on the same basic terms", he told the press conference.
"I believe that it would be best if we could begin to lift lockdown through a set of common measures, implemented to a common timetable".
Legislation requires the Welsh Government to have a formal review of lockdown measures every 21 days.
Mr Drakeford said it was essential that people in Wales "feel any changes we make are safe for them and their family."
He said it was also important not to throw away the “extraordinary sacrifices” people have made so far.
Watch the full briefing from the First Minister here
Mr Drakeford said the number of people in hospital with Covid-19 across Wales has fallen from 1300 on April 23rd, to just over 1000 on May 4th.
He said there were now fewer than 100 people in critical care beds in Wales with the virus - down from more than 160 in mid April.
Mr Drakeford said these figures showed lockdown measures "have helped us to move past this peak."
But he warned that ONS data showing more than 1000 people have now died with the virus in Wales was "a sombre milestone."
He stressed that the early stages out of lockdown "will not look very different to lockdown itself."
Asked whether Wales might look to adopt a contact-tracing app due to be trialled on the Isle of Wight, Mr Drakeford said the Welsh Government is "working with the UK Government" to see whether the app could be used in Wales.
The app, which the UK Government says would need to be downloaded by half of the population to work, could alert users when they have come into contact with someone who has coronavirus symptoms.
Mr Drakeford said there were issues to be resolved, "particularly issues to do with data, personal data, how that data can be shared."
But he added: "If we can solve those issues, and if we can solve them in a way that people would be willing to share their data and feel secure in doing that, then I see advantages in being part of that wider app. But we're not quite there yet."
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