The First Minister has said he hopes to be able to provide an update next week on how people in Wales could safely see their family and friends.
Mark Drakeford said he understands "that the thing [people] are missing the most is human contact with family and friends."
He said the Welsh Government is actively looking to see whether there are models that would allow people to safely see loved ones - but added any changes could only be implemented provided they did not compromise people's safety.
He told the daily briefing: "We’re not there yet in terms of being sure of how that might best be delivered, but it’s the most active of our discussions.
"We’ll be talking about it again this afternoon and I’m hopeful we’ll have something to say on that next week."
Watch First Minister Mark Drakeford's full update below
Mr Drakeford also paid tribute to the 500 Welsh volunteers who will be participating in the Oxford University Covid-19 trial, as well as more than 1,500 people across Wales who are participating in research to investigate the virus and find potential treatments.
He said: "Ever since I was Health Minister, I have always been hugely impressed by the willingness of Welsh people and patients to take part in clinical trials. The motivation is always the hope that benefit will come from it for others. We are very fortunate still to have in Wales that sense of looking out for one another."
Mr Drakeford also said four small contact tracing trials will begin this weekend in the Cwm Taf Morgannwg, Powys, Betsi Cadwaladr and Hywel Dda health board areas. The trials will involve contacting people who have tested positive for coronavirus.
Mr Drakeford also shed light on new antibody tests which are set to be rolled out across Wales and the rest of the UK. He said healthcare settings and care homes will be prioritised as these tests become available.
The First Minister described the vaccine trial and the various ongoing research studies as offering "hope of new treatments and a future free of coronavirus."
But he reiterated the importance of following the stay-at-home rules for the time being, particularly ahead of the bank holiday weekend.
He also issued a reminder that new, tougher fines are now in place for those who repeatedly break the rules.
"I continue to ask everyone in Wales to play their part and protect themselves, their loved ones and friends by following the stay-at-home rules.
"This is as ever particularly important as we approach another bank holiday weekend in Wales.
"New tougher fines are in place for that small minority of people who repeatedly break the rules.
"We have made some small changes to the rules in Wales – we have lifted the once-a-day restrictions on exercise but please stay local and stay safe.
"All the evidence shows that efforts everyone have made are having a real impact on the spread of the virus, but making too many changes too quickly to the regulations could put that progress in peril".
The lockdown in Wales is set to be reviewed again at the end of next week based on the latest scientific evidence.
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