Wales will join Scotland in continuing the lockdown restrictions for the next three weeks..
First Minister Mark Drakeford told a press conference in Cardiff the latest evidence showed the first peak of coronavirus infections had been passed in the country, but lifting the restrictions too soon would lead to a "return of the virus".
He added some "small" adjustments have been made to the restrictions, ahead of changes for England due to be announced by Boris Johnson on Sunday.
Exercise will be allowed for more than once a day, but it must start and end at home. Garden centres will also open with the two-metre social distancing rules observed. This will be effective from Monday 11 May.
It comes as a further 28 people in Wales died after testing positive for coronavirus.
Mr Drakeford reiterated that people must continue to work from home where possible, only travel if absolutely necessary, continue to observe the two-metre social distancing and wash hands regularly to "continue to protect us all from coronavirus and save lives."
Mr Drakeford also announced local authorities should look at letting libraries and recycling centres reopen. He said the changes will apply to everyone but the 120,000 people classed as vulnerable and more at risk of the virus in the shielding group must continue to follow more strict advice.
His announcement was welcomed by opposition parties including the Plaid Cymru leader Adam Price who also urged the Prime Minister to be as cautious with his announcement for England.
He said, "We welcome the cautious approach adopted by the First Minister in his statement today and implore the UK prime minister not to implement an England-wide relaxation of restrictions that would completely undermine this approach and potential have a disastrous impact on Wales."
Watch the press conference in full:
The lockdown was introduced in Wales to help slow the spread of coronavirus and reduce hospital admissions.
10,851 people have contracted the virus in Wales with 1,062 deaths. The First Minister said that without the tight restrictions in place that limited people's movements, "many more people" would have died.
Wales' Chief Medical Officer said that the lockdown has helped "flatten the curve" of the virus, but if the lockdown is lifted too soon, then there is an increased risk of a second wave of transmission.
During the press conference, Mark Drakeford presented a slide which showed the "R rate" was more than two before the stay-at-home restrictions were introduced in March.
It is between 0.7 and 0.9 now. He said, " If we lift the measures too quickly, the R rate will increase."
He said the Welsh Government would watch the level "like a hawk" and reimpose any restrictions if it began to rise to previous levels.
Ministers in Wales must review the need for the lockdown requirements and restrictions in the regulations every 21 days.
Mr Drakeford said he spoke with the prime minister yesterday who "emphasised his wish to move in the most careful and cautious way".
He said the "four nation approach" of all UK governments working together was working and the system we have is "showing its strengths".
He added he did not think there were mixed messages between what Wales is doing and what the Westminster government was planning.
"I don’t believe you will see anywhere in the UK other than the most modest of immediate changes broadly of the sort I have proposed in Wales."
On the reopening of schools, the First Minister said, "I said a week ago it needed three weeks from the point you make the decision to schools reopening which takes us to June - and we are not making that decision for the reasons I have set out."
Mr Drakeford finished his press conference by saying, "coronavirus is with us not just for May, June or July.
"It will be with us for many months to come - we will have to be planning for those three months but we have to plan way beyond that to find the best way through this."
Analysis from Political Editor Adrian Masters
The agreement between the UK's different governments on how to tackle the coronavirus crisis has faltered this week, but looks like it'll remain mostly in place after this weekend's flurry of lockdown announcements.
Mark Drakeford's cautious approach will almost certainly be similar to that taken by the Prime Minister when he spells out any changes for England on Sunday. There'll be none of the talk of 'freedom' that some were predicting earlier in the week.
They may use different terms - Boris Johnson may talk about a 'phased roadmap' for instance rather than 'lockdown' - but I expect the reality to be the same pretty much the same.
So there's unlikely to be any need to worry about keen gardeners in England driving over the border to garden centres here, because they'll probably reopen on both sides.
The working relationship between the four governments has been unexpectedly strong - given the different political parties running each of them - but it has frayed at the edges in the run up to this announcement.
Not that cooperation has ended. Far from it. As Number 10 confirmed, officials are talking again today. In fact they haven't stopped communicating with each other.
Where things seem to have broken down is between ministers. Nobody blamed Boris Johnson for taking time off after his illness but taking two weeks after returning to work to speak to the First Ministers of Wales, Scotland and the two leaders of Northern Ireland may come to be seen as a mistake because it's those sort of conversations that iron out any wrinkles that may be emerging.
In the run up to the first review of the lockdown three weeks ago, senior ministers in the four governments spent a week talking to each other before agreeing unanimously.
This time they seemed to be speaking but not hearing each other. UK Government ministers highlighted concerns about the health and economic impacts of lockdown while devolved ministers focussed on the risks of lifting too early. On both sides of the divide, there was frustration but they've ended up in essentially the same place.
But there will be differences, however slight they may be, and there's not acceptance of that by the leaders. In his phone call with the First Ministers yesterday, Boris Johnson said the UK-wide approach wasn't undermined "if different parts of the UK begin to move at slightly different speeds. Those decisions will be made based on the science for each nation."
And Mark Drakeford today said that devolution "is showing its strengths" in the coronavirus crisis. Governments make the big decisions together and take different decisions depending on the situation on the ground that they're facing.
What he will have to do is set a road map for a way out of the current state of lockdown, something Boris Johnson is expected to do on Sunday.
The First Minister has previously set out what the thinking will be behind any decision to ease individual rules - long before the UK Government if you're keeping track of that sort of thing. But he hasn't given the sort of details and possible timetable that the Prime Minister is likely to.