Humza Yousaf said there was room to “maximise” the vaccine rollout, particularly of second doses increasing the number administered each day.
It comes after a Public Health England (PHE) study found that both jags were almost as effective against symptomatic disease from the B1617.2 Indian strain as they were against the Kent variant after the second dose.
However, they were only 33 per cent effective against the Indian variant three weeks after the first dose, compared with about 50 per cent against the Kent strain.
Mr Yousaf said: "The really important message I took from the Public Health England study was that actually the effectiveness of the vaccines drops a little if it's just after the first dose, that enhances the importance of the second dose.
"In my first few days as Health Secretary I met with a number of people involved in the vaccine roll-out - I'm actually due to get my vaccination first dose tomorrow myself - and having discussed it with them, I do believe there is a possibility of maximising our vaccine roll-out, particularly the second doses, amongst those priority groups.
"So while we're doing extremely well, I think there is room in the coming weeks to increase the number of vaccines that we're administering per day and per week."
Scotland has recorded 378 new cases of coronavirus but no further deaths in the last 24 hours, according to latest figures.
It means the death toll under this daily measure – of people who first tested positive for the virus within the previous 28 days – remains at 7,664.
Figures published by the Scottish government on Sunday showed the daily test positivity rate was 2 per cent, up from 1.8 per cent the previous day.
So far, 3,108,819 people have received their first dose of the Covid-19 vaccination and 1,828,930 have received their second dose.
Glasgow is the only area in Scotland to remain in Level 3 of Scotland's coronavirus restrictions, with the highest coronavirus rates in the country at 126.7 per 100,000 people in the seven days to May 19.
First Minister Nicola Sturgeon announced on Friday that the area would be staying in Level 3 for at least one more week as they had “not yet turned the corner” to curb the rising case numbers in the area.
Mr Yousaf said that he hoped that after a week of further restrictions in Glasgow it would be clear whether higher case numbers had led to a rise in hospital and ICU admissions.
He said: "If the answer to that – which I hope it is – is no then of course we can look at what we can do in terms of easing restrictions in the future."
People aged 18 to 39 who live in postcodes G41, G42, G5, G51 or G52 in the southside of Glasgow are being offered coronavirus jags early as public health authorities tackle a surge in cases in those areas.
Asked whether having vaccine surges in some areas means some people in other areas will have to wait longer, Mr Yousaf said that should not be the case.
He said: "I think the vaccine roll-out right across the country is going extraordinarily well, I get a breakdown of vaccines per health board and right down to local authority level and I can see no slowing down in the figures that come to me.
"We actually have a good supply of the AstraZeneca vaccine and I'm hoping that using that, plus I think we could probably be a bit more proactive – in Glasgow a social media call went out to people to come because there was additional vaccine supply available, that was very well received – in the coming weeks, my hope will be to increase the number of vaccines going into people's arms."
The PHE study, which took place between April 5 and May 16, found that the Pfizer vaccine was 88 per cent effective against symptomatic disease from the Indian variant two weeks after the second dose, compared with 93 per cent effectiveness against the Kent strain.
Meanwhile, the AstraZeneca jab was 60 per cent effective, compared with 66 per cent against the Kent variant over the same period.
UK Health Secretary Matt Hancock described the outcome as "groundbreaking", while PHE said it expects to see even higher levels of effectiveness against hospital admission and death.
He said: "This new evidence proves just how valuable our Covid-19 vaccination programme is in protecting the people we love.
"We can now be confident that over 20 million people - more than one in three - have significant protection against this new variant, and that number is growing by the hundreds of thousands every single day as more and more people get that vital second dose."
Dr Jamie Lopez Bernal, consultant medical epidemiologist at PHE and the study's lead author, said there was more confidence in the data from the first vaccine dose compared with that from the second.
He said: "There are bigger numbers that have been vaccinated with one dose. So I think we classify that as moderate certainty around the first dose, but low levels of confidence around the second dose."
However, Professor Susan Hopkins, PHE's Covid-19 strategic response director, said the data trend was "quite clear" and was heading in the "right direction".
PHE said the difference in the effectiveness between the vaccines may be due to the AstraZeneca second dose being rolled out later than the Pfizer vaccine.
Data also shows it takes longer for the AstraZeneca jab to reach maximum effectiveness.