Up to 400,000 people could be given the Covid-19 vaccine every week by the end of February, Scottish Health Secretary Jeane Freeman has told MSPs.
Health teams are ramping up the rollout of jabs, with 1,100 vaccination centres now open and using two vaccines.
Ministers aim to vaccinate care home residents, NHS staff and over-80s by the first week of February.
They then hope to have completed the over-70 group by mid-February and over-65 and vulnerable groups by March.
This would see 1.4m people given the jab, and Ms Freeman said the government's "priority is to vaccinate as many people as quickly as possible".
However, the BMA Scottish GP Committee has warned the vaccine supply is "stuttering" and blamed "bureaucratic hold-ups" for delaying distribution.
In a statement at Holyrood, the health secretary said Scotland faces "a more perilous situation than at any point in this pandemic", with the new variant of coronavirus "increasing in its dominance" of infections north of the border.
However Ms Freeman said there was hope in the form of the vaccination programme, which she said was "scaling up rapidly".
A first dose of vaccine has now been given to just over 80% of care home residents and 55% of staff, along with 52% of frontline NHS staff.
And in the eight days since 4 January, just over 2% of those aged 80 or over in the community have been given a first dose.
Ms Freeman said that age was "the greatest risk factor for serious illness and death from Covid, and represents well over 90% of preventable mortality".
The government is prioritising giving a first dose to as many people as possible, which Ms Freeman said provides "very high protection", with a second dose of the same vaccine then administered within 12 weeks.
Ms Freeman said that by the end of February, an average of 400,000 people should be getting a jab per week.
The government is also working to set up large vaccination centres in the community, which could handle up to 20,000 vaccinations a week in a single location.
Sites include the Event Complex conference centre in Aberdeen, Ravenscraig Regional Sports Facility in Motherwell, Queen Margaret University in Musselburgh and the Edinburgh International Conference Centre, and Ms Freeman said work was ongoing to secure more centres in the Glasgow area in particular.
A total of 4.5m adults in Scotland are in line to be vaccinated.
Ms Freeman said she was aware that people would "want to know when it will be their turn", saying a national advertising campaign would be established to "inform the public".
Scottish Conservative health spokesman Donald Cameron said it was "clear not enough people are being vaccinated each day and timetables are slipping".
He also asked Ms Freeman whether there were delays to the creation of a national booking system, after speculation that it could hold up the start of mass vaccinations.
The health secretary said she did not believe it was the case that timetables were slipping, and said there were no delays to the national booking system - adding that it would be "ready from the beginning of February to do its job".
Meanwhile Scottish Labour's Monica Lennon asked how quickly the country could move to a 24 hours a day rollout of vaccines.
'People are anxious'
Ms Freeman said this was "entirely possible" once the mass vaccination centres are open, saying she "would anticipate that would be by the end of February or early March".
She said: "The will is there to do that, if that is what it takes, because the objective is to get as many people vaccinated as possible."
The BMA Scottish GP Committee has said practices "don't know when their next supply is coming in".
Its chairman, Dr Andrew Buist, told BBC Scotland's Drivetime programme the Scottish government "must do everything possible to ensure vaccine supply is as good as it can be".
He said: "I've spoken with the chief medical officer about this and emphasised we should remove any bureaucratic hold-up to the distribution of this vaccine.
"People are obviously very anxious to get it as soon as possible.
"We know what the priority groups are, we have the practices ready and running to give it to their patients. We just need to get the vaccine to them."