People need to know that the recording of coronavirus deaths "can be relied upon", Wales' first minister has said.
Mark Drakeford said he would receive a report on the under-reporting of deaths in north Wales on Monday.
The investigation was launched after it was revealed that Betsi Cadwaladr health board failed to report numbers daily for a whole month.
Mr Drakeford also defended a delay in launching an online booking system for coronavirus tests for key workers.
Speaking on the BBC's Politics Wales programme, he said further "systems" were becoming available to increase testing for key workers, rising from 1,300 tests to 1,800 available daily this week.
He said the number of tests being taken up had been rising but there was more work to do to make sure all of the testing capacity was being used.
Last Sunday, Mr Drakeford said he hoped the online booking system would "be up this week".
But he said this Sunday that it had been tested over the last week "to make sure it will withstand the pressure" it could face from workers trying to get a test and would be used "more extensively" next week.
He said a similar system in England had "fallen over" within hours of being used.
Concerns have also been raised about the system for recording the number of coronavirus deaths in north Wales.
On Thursday, Betsi Cadwaladr health board reported 84 deaths across north Wales between 20 March and 22 April.
It resulted in a jump of 110 in the total confirmed deaths with coronavirus in Wales - the biggest daily increase in the figures.
The health board said the delay was due to issues with its reporting system.
Public Health Wales has repeatedly warned the number of deaths could be higher than figures showed, as they only included the deaths formally reported to them, those who died in hospitals, and some care homes, and whose tests were analysed in a laboratory.
Plaid Cymru said an "urgent explanation" was needed, whilst the Welsh Conservatives said it "smacks of incompetence of the highest level".
Mr Drakeford said: "Ministers are entitled and the Welsh public is entitled to know that the figures that Public Health Wales publishes every day are as accurate as they can be.
"I have asked for a report that will be on my desk tomorrow so that I can be sure that any glitches that have been there are being ironed out.
"I understand that Public Health Wales publishes the figures every day, they are doing it urgently, they always say those figures are subject to review.
"But I need to know, and people in Wales need to know, that those figures can be relied upon and I expect to have that confirmed to me tomorrow," he added.
On Friday, the Welsh Government published a framework for the lifting of coronavirus lockdown restrictions, which will be done in phases, "like a traffic light" moving from the red zone to amber and then to green.
Asked whether some restrictions could last potentially for a year, the first minister said: "I don't see us going back to places where there is the biggest risk - mass gatherings, that sort of thing.
"There will be some things that we will only get back to doing right at the end of the process.
On personal protective equipment (PPE), Shavannah Taj from the Wales TUC told the programme her union was hearing "real horror stories" about care workers using makeshift equipment.
She added: "We've had examples given to us, this week alone, where a care worker was told that if you run out of aprons, best bet for you is to use some black bin liners and make your own."
Mr Drakeford said he was "confident" there was enough PPE in the system "to take us into next week".
He said there was a shortage of fluid-resistant gowns across the UK and Welsh workers had enough for a further week, but stores needed to be replenished.