More than half of Scotland's over-80s have now had a first dose of Covid-19 vaccine.
The latest figures showed that 51% of people in the age group have been vaccinated - considerably lower than the 78.7% across the UK as a whole.
Opposition parties said the number of people being vaccinated every day has actually fallen over the past week.
But deputy first minister John Swinney insisted that good progress was being made.
Mr Swinney also said that the country remained on track to hit its target of giving a first dose of vaccine to care home residents and staff, NHS workers and the over-80s in the first week of February, and then over-70s by the middle of that month.
Mainland Scotland and a number of islands have been in the top level of restrictions since Boxing Day, with a "stay at home" lockdown in place since early January.
The Scottish government cabinet met on Tuesday and formally confirmed that these restrictions will remain in place until at least mid-February, with Mr Swinney warning that "the position in Scotland remains precarious".
He told MSPs that case numbers were falling and hospital admissions "may be starting to stabilise", but said that any relaxation of restrictions could see them rise again.
The deputy first minister said that the vaccination programme was now playing "an increasingly vital role in keeping the virus under control".
He said: "In time - not immediately, but in the fairly near future - vaccination should start to significantly reduce the number of people who die from Covid.
"In the longer term, as more and more people are vaccinated, we should see an impact on hospital admissions and transmission rates.
"And of course ultimately the vaccination programme - combined perhaps with some continuing restrictions - offers us a way out of this pandemic."
The vaccination programme has now seen 95% of older care home residents and 98% of frontline health and social care workers in Scotland given a first dose, along with 51% of people aged 80 or over.
Wales has vaccinated about 52% of its over 80s - with poor weather being blamed for that figure not being higher - while in Northern Ireland said on Sunday that it had vaccinated about 55% of people over the age of 80.
The Scottish government has said the focus on care homes - where vaccination is more labour-intensive and time consuming - was why it has lagged behind the other UK nations in the over-80s group.
However, the Scottish Conservatives said that the "slow and sluggish" response in Scotland was actually because supplies "are just not getting out to GPs quickly enough".
The Tories said the daily number of vaccinations in Scotland peaked at 25,327 on 20 January before falling in five out of the next six days - with Tuesday's figures showing that a total of 22,498 people had been vaccinated in the previous 24 hours.
The party's leader, Douglas Ross, said: "The SNP's vaccine rollout is behind schedule and it's entirely their fault.
"The SNP have hundreds of thousands of doses sitting in storage, ready to be used, but they're failing to deliver. The pace should be picking up, not standing still.
"Their own plan says the vaccines are available for overnight delivery but GPs are still telling us they're not getting supplies quickly enough."
Scottish Lib Dem leader Willie Rennie said the government's explanations "simply do not add up", and that "the programme in England is getting faster while in Scotland it's getting slower".
Mr Swinney insisted the government was "on course" to hit the target of completing this group by the end of the first week of February.
He said: "Good progress has been made on the delivery of the vaccine for over-80s. We have got to 95% on care home residents, who are most at risk of morbidity from Covid.
"We are in a majority now in over-80s and that task will be completed by the end of the first week in February, and we will move onto the next priority group and complete that by the middle of February as announced."
The deputy first minister also said the Scottish government would "go at least as far as any UK government announced in enhancing quarantine arrangements", with an announcement expected later on the use of quarantine hotels for international travellers.
He said ministers would also look at "additional supervised quarantine measures that can further protect us from importation of the virus" in the coming week.
The Scottish Greens have called on the government to consider the use of quarantine hotels for Scottish residents who "do not have the financial or practice resources to self-isolate" at home.
Mr Swinney also announced £30m of extra funding to support further education during lockdown, including £10m for colleges and universities to replace lost income and £20m in hardship payments for students.