People will be able to exercise outside more than once a day in Wales and some garden centres set to reopen, First Minister Mark Drakeford has said.
Announcing only “modest” changes to the coronavirus lockdown, Mr Drakeford warned it was “too soon” to go further.
The rest of the stay-at-home restrictions will be extended for another three weeks until 28 May.
It comes 48 hours before Prime Minister Boris Johnson announces a “roadmap” for easing the lockdown in England.
But a UK government minister said there would be no “dramatic overnight change” to restrictions.
Earlier, Nicola Sturgeon urged people in Scotland to stick to lockdown restrictions and stay at home over the bank holiday weekend.
The changes to the seven-week-old lockdown in Wales come into force from Monday.
Mr Drakeford warned anyone thinking of travelling to beaches or mountains that they will be stopped and sent home.
“We must not lose the progress we have all made,” he said in a special broadcast on Friday evening.
“All of us must continue to work from home wherever we can. All of us must only travel when absolutely necessary.”
Despite reports of tensions between the different governments, Mr Drakeford said he wanted to “move in step with the other nations of the United Kingdom”.
He told a press conference that just a small increase in the rate of transmission of the coronavirus – the so-called ‘R’ number – would mean thousands more in hospital and as many as 7,200 deaths.
So far at least 1,285 deaths involving Covid-19 have been registered in Wales, as of 24 April, according to the Office for National Statistics.
Lockdown rules must be reviewed every three weeks – the next review of regulations in Wales have to take place by 28 May.
He said the Welsh Government believed that, as a result of the latest three week review, small changes to the regulations could be made.
From Monday, people will be allowed to exercise more than once a day, but will be told not to travel “a significant distance” from home.
Exercising more than once a day has been illegal in Wales since the start of the lockdown, but not in England.
Garden centres will be allowed to re-open, provided they can ensure the two metre social distancing rule is followed.
Councils will begin to work on plans to re-open libraries and household waste centres.
The 120,000 people in the most at-risk groups, who have received official “shielding” letters, should continue to follow that advice.
Calling them “modest adjustments”, Mr Drakeford said they would “make a difference in people’s lives”.
Mr Drakeford said the R number stands at around 0.8 in Wales. Welsh Government estimates suggest that, at this level, 800 may die from coronavirus between 8 May and 7 August.
But he warned that if this rose to just 1.1, “we would see 7,200” deaths.
The first minister explained the Welsh Government believed the R rate in care homes is higher than in the community more widely – although said it was harder to be precise.
Will the prime minster’s announcement be similar?
The first minister believed Mr Johnson’s lockdown announcement for England on Sunday will be “broadly” similar to Wales’.
Mr Drakeford said announcing changes in Wales ahead of the prime minister’s public address was “not an attempt to place any restraints” on Downing Street.
‘Unease’ if PM sets timetable – Felicity Evans, BBC Wales political editor
The Welsh Government is all about the message and it’s still “stay at home”, despite the minor relaxations they’ve just announced.
That’s why Thursday’s newspaper headlines trumpeting the end of the lockdown in England alarmed Welsh Government ministers, who were wondering how they could enforce two such different approaches on the densely-populated border.
After a phone call with the prime minister, Mark Drakeford seems to have been reassured that any adjustments Boris Johnson does announce on Sunday will be modest and cautious – just like in Wales.
But what about the next steps? If the prime minister sets out a timetable, along with dates, for possible further easing measures in the future, the Welsh Government is likely to be uneasy about the message that might send.
The first minister will be discussing exit plans from lockdown over the weekend with UK ministers at a meeting of COBRA.
Mr Drakeford said there would be a need to “spell out” a roadmap on the way ahead – the UK government is expected to begin to do so on Sunday.
He added: “We will be listening carefully to what the prime minister has to say when he makes announcements on Sunday evening.”
The Welsh Labour leader said the Welsh Government “will be a part of that conversation” and “will set out how that will be put to work here in Wales”.
Talks between the Welsh and UK government over coronavirus have taken place “in fits and starts”, he claimed.
Mr Drakeford spoke to Mr Johnson on Thursday, but has called for more regular formal meetings as the crisis continues.
In response to the Welsh Government announcement, Downing Street has said the UK government remains committed to a four-nation approach to lockdown “wherever possible”.
The PM’s spokesman stressed any “easement that we do make will be very limited” and added that Boris Johnson had had constructive talks with devolved leaders on Thursday.
Environment Secretary George Eustice told the daily UK government news conference the PM would set out a “roadmap of how we can evolve the current restrictions that we have”.
“We will be very very cautious as we loosen the restrictions we have,” he added.
Asked about the Welsh Government’s announcement, Mr Eustice said: “I don’t think we need to get too worked up about timings.”
The Welsh Local Government Association said recycling centres would not reopen immediately as each council will use its discretion to decide if it is safe to do so.
Plaid Cymru leader Adam Price welcomed the announcement and called on the prime minister “not to implement an England-wide relaxation of restrictions that would completely undermine this approach and potentially have a disastrous impact on Wales”.
Welsh Conservative Senedd leader Paul Davies said: “While I recognise that decisions on the lockdown in Wales are a matter for the Welsh Government, it is vital that governments across the UK coordinate their efforts as much as possible to avoid confusion amongst the public.”
But Brexit Party Senedd leader Mark Reckless objected: “The reason Coronavirus will be with us far beyond July is the government dragging this out, destroying our wellbeing, lives and the economy”.
Business lobby group, CBI Wales, said getting Wales back to work “will minimise the impact on livelihoods from a crisis that has shaken the global economy”.
“It must be done gradually, based on science, to avoid a devastating second wave and retain public confidence. Moving too far, too fast could set back the economic restart,” said director Ian Price.
Analysis by Vaughan Roderick, BBC Welsh Affairs Editor
This was an attempt to row back from the sort of news stories – and these haven’t come from Wales, they’ve come from Westminster – that there was going to be a major relaxation of the lockdown rules.
Yes there are some changes, like being allowed to exercise outside more the once a day, but the new message we heard there was as well as stay at home, stay safe and stay local.
Mark Drakeford denied this was an attempt to put pressure on Boris Johnson, but he knows perfectly well, and Nicola Sturgeon knows perfectly well, that this does put pressure on Boris Johnson.
Because these are governments saying, if you relax too far thousands of people will die; in England that equates to tens of thousands of people.