Nicola Sturgeon claimed Scotland is on course to have one million people vaccinated this week.
The First Minister made the claim as she provided an update report on covid vaccine rates.
SNP Health Secretary Jeane Freeman said last year she hoped the target would be met by the end of January.
The Scottish Government has since faced intense criticism over the number of people who received a jab, compared with other parts of the UK. However, the numbers shot up last week.
In her televised briefing today, Sturgeon said 27,557 vaccines had been administered yesterday - three times the number of the previous Sunday.
She said 866,823 people had now received received a first dose: "Over the course of this week, we expect to hit the milestone of one million vaccines administered."
Sturgeon said a total of 99.6% of residents in older care homes have received a first jab, which is “a scale of uptake which none of us really believed would be possible”.
The First Minister added that more than 95% of over 80-year-olds living in the community have had their first dose of a vaccine and almost 67% of people aged 75-79 and 29% of people aged 70-75 have received a first jab.
Highlighting that more than 290,000 people have received a first dose in the past seven days, Sturgeon said Scotland’s vaccination programme “undoubtedly picked up pace considerably over the course of the last week”.
But she warned the first dose of a vaccine does not begin to have a protective effect until around two or three weeks after it is received and urged everyone, including those who have received it, to be careful and stick to lockdown restrictions.
The First Minister also gave an update on the daily coronavirus case figures in Scotland.
A total of five deaths of coronavirus patients in Scotland have been recorded in the past 24 hours, along with 928 new cases.
The death toll under this measure – of people who first tested positive for the virus within the previous 28 days – is now 6,443.
The daily test positivity rate is 6.6%, down from 6.9% on Sunday when 584 new cases were recorded.
There are 1,672 people in hospital confirmed to have Covid-19, down 38 in 24 hours.
Of these, 108 were in intensive care, no change on the previous day.
Sturgeon also announced an expansion of targeted community testing using rural fire stations to a total of 21 locations in the coming weeks.
