It is not yet clear if a pledge to vaccinate 70% of over-80s and those in care homes has been reached, Wales' health minister has said.
Vaughan Gething said it would not be known for the "next day or two" if the target - which was due to be hit by the weekend - was met.
More than 270,000 people have had their first dose of the vaccine.
He said the programme had "gathered pace," with a "sharp acceleration" in the vaccines given.
Figures show that 8.6% of Wales' population had been vaccinated in seven weeks.
This is currently above both Scotland (7.6%) and Northern Ireland (8.4%), according to latest figures.
Asked why the daily figure - 6,295 - was so low, the Welsh Government said it was a combination of a delay in data entry and verification over the weekend and snowfall, which closed four vaccine centres.
A spokesperson said: "Data takes time to feed through to us, and snowfall meant some centres and GP clinics were closed, and people chose to reschedule their appointments this weekend.
"A massive amount of work was done last week and will be done this week. We fully expect to catch up with those missed appointments this week, with tremendous effort being made over the next 48 hours."
Wales' opposition parties welcomed the increase in vaccination rates in Wales over the past few days, but warned there should be no "let-up" going forward.
Last week, Mr Gething was criticised after he said a majority of over-80s had been vaccinated when they had not - he later said he made a mistake.
The latest Public Health Wales figures show 270,833 people have had their first dose of the vaccine, including 88,005 of over-80s - or 48.1%.
However Mr Gething said there was a "lag" in the statistics.
Health officials say this is to allow verification and quality assurance work on the figures, which have to be inputted by GP clinics carrying out the immunisation. This work can take four or five days.
Based on the latest figures, Wales needs to give first doses to about 23,500 people a day to meet its target of reaching the four priority groups by mid-February.
In the Senedd last Tuesday Mr Gething said he expected 70% of over-80s in Wales, and 70% of care home residents, to receive their first jab by the end of the weekend.
At the press conference the minster said: "We don't have all the data back from the vaccination centres and GP practices around Wales."
He hoped to publish the data by Wednesday.
More than 70% of care home workers had been reached, he said, and all 16 GP practices in Powys will start vaccinating this week.
The health minister said some people in their 70s were getting the vaccine ahead of those in the over-80s bracket because of the progress that had been made.
"Because we've made such good progress in vaccinating over-80s in large parts of Wales... some health boards are able to make progress with that part of the programme," he said.
Mr Gething added that Wales was "on track" to offer vaccines to the top four priority groups by mid-February.
Vaccinating more than 20,000 people each day is "what we can do on a regular basis if we have the supply," he said, saying they were aiming to vaccinate "north of 140,000 each week on a regular basis".
The new Conservative leader in the Senedd, Andrew RT Davies, said it was "really good to see that everyone's pulling together to get this ramp up in the rollout of the vaccine" but warned that "it's all got to be repeated again" in providing the second dose.
"Everyone is going to have to have a second vaccination and the energy and effort that's going to be required in that is going to be huge, and that's why we keep calling for a vaccination minister to be at the heart of this to ensure that there is no lack of energy, no lack of decision-making energy, within this rollout."
Plaid Cymru leader Adam Price said that it was "great to see the heroic efforts over the last few days, and this huge acceleration in the rate of vaccination is very welcome".
But he said it was "very important now that we see no let-up, because whether or not the Welsh Government has met the target, there will still be many people in Wales in the top priority group that will want to be vaccinated yet."