Wales has become the first UK nation to offer the coronavirus vaccine to everyone in the first four priority groups, the First Minister has confirmed.
Although Mark Drakeford said the race is not between nations but "between the injection and the infection".
He said the milestone was a "truly phenomenal effort" for the country's vaccination rollout, which has so far seen 684,097 people receive their first dose.
Mr Drakeford promised residents and staff in care homes for older adults, frontline health and social care workers, all people aged 70 or over and clinically extremely vulnerable individuals would be offered the jab by mid-February.
It comes after Wales failed to meet an earlier target of vaccinating 70% of the over-80s by January 24 - only managing 52.8% by that time.
Health Minister Vaughan Gething said "not everyone in these groups will have attended their appointment yet", and that "some will not have responded and some will have chosen not to have the vaccine".
He added that the Welsh Government is now looking ahead to meet the next milestone, including to complete the vaccinations of those in the next five priority groups by the spring.
Addressing concerns that not everyone in the four priority groups has received their invitation, a Welsh Government spokesperson has said it is confident Wales will have administered coronavirus vaccines to "every single person that wants a jab" in its top four priority groups by the end of the weekend.
The spokesperson said the Government expects to reach this target by the end of Friday, but there may be "mopping up" over the weekend to arrange appointments for those from the priority groups who had missed or previously refused a slot.
Mr Drakeford said at Friday's press briefing there may be "a whole range of reasons" why some people prioritised for the vaccine may not have yet been reached.
He said: "Every part of Wales is spending this week checking and re-checking whether there are any people who may have been missed.
"There may be a whole range of reasons why that could have happened and I couldn't really speculate on them.
"Part of my purpose in doing the press conference today is to say anybody who knows of somebody who may have missed out, it is not too late at all.
"We will make sure that those people have an appointment, they will get it as fast as possible."
Mark Drakeford told BBC Radio 4's Today programme that people aged over 50 would receive invitations for vaccine appointments from Monday.
He said: "Because we will have completed the first four groups by this weekend, then, as from Monday, people in the next five groups - that's people aged over 50 - will already be booked in for their appointments next week.
"So I know that people in those groups will have already been contacted this week by practices, by mass vaccination centres, and those people will be getting their vaccine from Monday onwards."
The Welsh Conservative's leader in the Senedd, Andrew RT Davies, labelled the achievement "a true British and Welsh success story".
He added: "I would like to thank everyone involved, especially our incredibly hard-working vaccination teams and armed forces who have gone above and beyond delivering the rollout programme.
"The UK Government's bold decision to opt out of the disastrous EU scheme has now been fully vindicated and ensured Wales has had the vaccines available to meet this target and protect the most vulnerable in our society.
"There is still a long road ahead of us with second doses still to be administered to those most at risk and over three quarters of the population requiring their first jab, but this is a significant milestone we can all celebrate as we look to recover from the pandemic and rebuild Wales."
In mid-January, the Welsh Government faced criticism for vaccinating fewer people in proportion to its population than the other home nations.
But on Wednesday, Wales became first UK nation to vaccinate more than 20% of its population, and one of the first countries in the world to do so.
However, Mr Drakeford has confirmed a planned reduction in vaccine supply is expected in Wales in the next few weeks.
At Friday's Welsh Government briefing, Mr Drakeford said the planned reduction would not affect anyone's appointment for a vaccine and would eventually allow the campaign to work faster.
"We know about this, it's a planned part of the programme and it is an issue that is the same right across the whole of the United Kingdom," Mr Drakeford said.
"We have factored this in to our vaccination plans. It won't affect people's appointments, it won't delay when people are due to get their second dose and it will allow us to go even faster later in the programme."
He told a Welsh Parliament committee on Thursday that one of the "challenges" of the Covid-19 vaccination programme in Wales was supply.
On Thursday, people in Cardiff were left queuing outside a vaccination centre after IT problems caused disruption at Cardiff and Vale University Health Board.
People with appointments, who were mostly over 70, found themselves queuing outside Splott vaccination centre in freezing conditions.
There were a further 25 suspected coronavirus deaths and 608 new confirmed cases, Public Health Wales data published on Friday revealed.
The agency's figures also showed that 715,994 people in Wales have now received their first dose of the coronavirus vaccine; 4,010 have been given a two-dose course.
Amongst the over-80s, 88.4% of people have now had a first dose of the vaccine.
In care homes, 80.3% of residents have now been vaccinated and 83.5% of staff have had a jab.
Wales' seven-day case rate now stands at 102 per 100,000.