Other countries such as Argentina and Ecuador have also reported elevated prevalence of the new variant.
Mark Drakeford warned that the new variant of Covid-19, known as the Delta variant, is now in widespread circulation in Wales and other parts of the United Kingdom, with numbers expected to rise.
"The most recent data show 99 per cent of sequenced and genotyped cases across the country are the Delta variant".
This is a rise of 173 cases since the last update on 14 June, with every health board in Wales reporting cases of the variant.
Of the 806, 527 (65%) were unvaccinated, 135 (17%) were more than 21 days after their first dose of vaccine, and 84 (10%) were more than 14 days after their second dose.
However, it points out that deaths tend to happen some weeks after an infection and it is therefore too early to judge the case fatality of Delta compared to Alpha or other VOCs.
"The increase is primarily in younger age groups, a large proportion of which were unvaccinated but are now being invited to receive the vaccine".
"The vaccination programme and the care that we are all taking to follow the guidance are continuing to save lives".
Dr Harries said: "It is encouraging to see that hospitalisations and deaths are not rising at the same rate, but we will continue to monitor it closely". We all must hold our nerve that little bit longer as our vaccine rollout continues and I urge everyone to keep observing hands, face, space and fresh air, and make sure you receive both doses of the vaccine for the best possible protection, he said.
The total number of deaths linked to Covid-19 in Northern Ireland since the start of the pandemic is 2,155.
There were 15,893 possible reinfections with SARS-CoV-2 identified up to May 30 in England throughout the pandemic, out of almost 4 million people with confirmed infections.
The REACT-1 study is an ongoing pandemic study, led by Imperial and carried out in partnership with Ipsos MORI, tracking current coronavirus infections in the community by testing randomly selected people each month over roughly a two-week period.