Humza Yousaf has said there is room to increase the number of coronavirus vaccinations in Scotland in the coming weeks.
The new health secretary said there is chance of "maximising" vaccine rollout, particularly of second doses.
He also stressed the importance of people receiving their second dose of a vaccine after a Public Health England (PHE) study found that both the Pfizer and AstraZeneca jabs were found to be almost as effective against Covid from the Indian variant as they are against the Kent variant after the second dose.
But they were only 33% effective against symptomatic disease from the Indian variant three weeks after the first dose, compared with about 50% against the Kent strain.
The MSP told BBC Scotland's The Sunday Show: "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 rollout - 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 rollout, particularly the second doses, amongst those priority groups.
"So while we're doing extremely well with the vaccine rollout, I think there is room in the coming weeks to increase the number of vaccines that we're administering per day and per week."
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.
People aged 18 to 39 who live in postcodes G41, G42, G5, G51 or G52 in the southside of Glasgow are being offered coronavirus jabs 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 told the programme: "I think the vaccine rollout 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.
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