The Health Minister Vaughan Gething said at the moment there are 822 people with coronavirus in hospital - this is 5% lower than last week.
During the Welsh Government daily briefly, Mr Gething said: "The majority of people being treated in critical care now do not have coronavirus, which shows more routine NHS work is taking place.
"There are 33 people being treated in critical care for coronavirus.
"About 22% of our acute hospital beds in Wales are currently empty."
Figures from the Office for National Statistics show the rate of excess deaths over the pandemic period in Wales is lower than in England and Scotland.
The Health Minister said that if Wales had seen the same excess death rate as England between March and early June, we would have seen an extra 1,600 deaths in Wales.
He added: "If England had the same excess death rate as Wales, there would have be almost 24,000 fewer deaths in England.
"We know that Wales, compared to England, has an older population; levels of underlying illness are higher and we have higher levels of deprivation so this is not what we would have expected to see at the start of the pandemic."
Ministers are reviewing the lockdown restrictions in Wales today. Any changes to the current rules are due to be announced tomorrow.
Most likely to be announced is some sort of return for non-essential retailso that high streets and shopping centres can start seeing the sort of socially-distanced queues that have been seen in England.
Vaughan Gething said he does not want to see "crowds bunched together outside shops" if non-essential retailers are allowed to open next week.
"People really do need to take a step back and realise the seriousness of the position we're in, and to recognise that the release from lockdown comes with responsibilities for all of us in the way that we choose to behave," he said.
He also warned "If we came out too quickly we could see a much deeper lockdown. We wouldn’t look to restart schools if it’s dangerous for children, parents and staff."
The Welsh Government has insisted that children will begin to return to schools here in Wales on 29th June as planned, but it will not put staff at ‘unacceptable risk’ of catching coronavirus.
It follows a survey by the UNISON union of thousands of support workers who said they were worried about returning to school too early.
Vaughan Gething said he understood those concerns and would ensure they are met but that it was important to balance the needs of staff and the needs of pupils.
Watch the coronavirus briefing in full: