But reports in newspapers suggesting lockdown could be significantly eased caused tensions with politicians in Wales and Scotland, who want a cautious UK-wide approach to any easing.
Later Downing Street conceded that the different UK nations may move at different speeds.
On Sunday morning the UK government’s Communities Secretary Robert Jenrick said it was the right time to “update and broaden” the message to the public from “stay at home” to “stay alert”.
“Stay alert will mean stay alert by staying home as much as possible, but stay alert when you do go out by maintaining social distancing, washing your hands, respecting others in the workplace and the other settings that you’ll go to,” he said.
Mr Gething, Wales’ health minister, emphasised it was an England-only message.
“I’ve seen the media briefings and changed message for England,” he said on Twitter. “There has not been a four-nations agreement or discussion on this.”
The Welsh Government’s message had not changed, he said.
‘We don’t agree’
Other members of the Welsh Government expressed dismay at the message. Deputy transport minister Lee Waters said: “We don’t agree with the change of message. It risks sending the wrong signal.”
“In Wales, the very clear message is to STAY HOME AND SAVE LIVES,” counsel general Jeremy Miles tweeted.
Asked about the new message on Politics Wales on Sunday, Mr Drakeford said: “Well I think it’s very important for people to be alert.
“People are going to be outside of the home more than they have been in Wales because we are reopening garden centres, allowing people to exercise more than once a day.
“But people need to be alert, to stick with social distancing, do all the right things.
“If you’re not doing one of the limited things on the list that takes you outside the home in Wales you should stay at home.
“That is still the way to keep yourself and others safe.”
‘Best answer to move in same direction’
Asked about whether he would set a roadmap, as expected in England, for exiting lockdown, he said he still believed “that the best answer is that we move in the same direction across the whole United Kingdom”.
But he said “it may be that the timings of exact measures will be different”.
Plaid Cymru’s Liz Saville Roberts will join other Westminster opposition leaders in a call with the prime minister on Sunday afternoon.
The party’s health spokesman Rhun ap Iorwerth called on the Welsh Government “to be much clearer about its engagement with UK government”.
“The Welsh health minister suggests there’s been no discussion about new England-only guidelines, yet in a TV interview today the first minister failed to say exactly what had and hadn’t been discussed. We can’t afford evasion and confusion,” he said.
In the same Politics Wales interview, Mr Drakeford said the Welsh Government will use the latest three-week lockdown extension to look at the possibility of opening more public services.
Mark Drakeford said potential options for discussion, include resuming some postponed NHS procedures and use of public transport.
He also said talks about when and how to reopen schools would also continue but repeated that there will be no change at the start of June.
But he said changes would made in a “careful and cautious way”.
“Certainly, in the Welsh Government, we would not be prepared to do anything that is signalled up to us as being a risk to the health of people in Wales,” he said.
On Tuesday, the Health Minister Vaughan Gething said keeping the rate of transmission of the coronavirus – the so-called ‘R’ number – will be the biggest factor in determining when the lockdown will be eased, with ministers wanting to keep R below one.
It was announced on Friday that ‘R’ stands at around 0.8 in Wales.
Asked where ‘R’ needed to be before further lockdown restrictions would be eased, Mr Drakeford said: “If we can hold that headroom [between R being 0.8 and 1] and increase it a bit further then there may be more things we can do.
“But it’s a matter of doing things, testing their impact in the community and then making decisions based on the best evidence you have at the time.
“Lockdown can’t go on forever both because it has other health impacts of its own… and, of course, lockdown does have an effect on the economy.”