The Welsh Government is sourcing spaces for temporary morgues as the current capacity "will not be sufficient" to deal with the coronavirus pandemic.
141 people have died after testing positive for Covid-19 in Wales, with the total number of confirmed cases standing at 2,466 as of 3 April.
The true number of cases is likely to be higher, according to Public Health Wales.
In March the health minister said 20,000 deaths are predicted in Wales in a "worst-case scenario".
First Minister Mark Drakeford said temporary capacity will be needed that "respects the dignity" of those affected by the virus.
He said: "The mortuary capacity that we have in the NHS to deal with ordinary times will not be sufficient to deal with the extraordinary pressures that we know are coming.
"So of course we are planning right across Wales, with the NHS, with our local government colleagues, with people who work in the funeral industry, to find some temporary capacity because we know it's going to be needed."
The First Minister also said the Welsh Government is changing the guidelines around funeral attendance.
At the briefing on Friday, he said the current regulations were "a bit too over-prescriptive".
He clarified that once families know how many people can attend a funeral it will be up to them to decide who goes.
Last month the Church in Wales announced funerals and baptisms could only go ahead if fewer than 10 people attend the service.
Speaking on personal protective equipment, Mr Drakeford said the Welsh Government has provided more than five million pieces to healthcare workers.
But he urged more Welsh companies to come forward and supply PPE.
It follows new guidance on when PPE should be used by frontline staff, outlining that it should now be worn when treating suspected, as well as confirmed, coronavirus cases.
Many heath and social care staff have expressed concerns about the availability of protective equipment.