First Minister Nicola Sturgeon has said there are grounds for "cautious optimism" that the lockdown measures are working.
At her daily briefing, Ms Sturgeon warned against complacency but said the figures on test positivity were the lowest for weeks.
The latest figures show 2,053 people are in hospital with Covid.
Ms Sturgeon said the deaths of 71 people who had tested positive had been registered in the past 24 hours.
There were 1,478 new cases and a test positivity rate of 6.9% - the lowest level for some time.
Ms Sturgeon's comments came as Office for National Statistics (ONS) figures suggest cases are decreasing slightly or levelling off across Britain.
During the week ending 16 January, about one in 100 people in Scotland had the virus.
For England the figure was one in 55 people, Wales was one in 70 and Northern Ireland was one in 60.
By 08:30 on Friday, 358,454 people had received their first dose of vaccine - up 23,500 on the previous day's figure.
The first minister said the vaccine programme was "picking up pace" and 34% of those aged 80 and over had now been vaccinated with their first dose. That would mean about 56,000 people in the age group had been given their first dose since Sunday, when the figure stood at 13.1%.
The target for vaccinating the remaining 175,000 people in the age group is 5 February, the same as the rest of the UK.
The first minister said 95% of residents in elderly care homes had now had their first dose, as had 77% of staff.
She said this accounted for the slower rollout of community vaccination for the over-80s but that this was now picking up rapidly.
Ms Sturgeon said Scotland had started with care homes because these were the people who were most vulnerable to getting ill and dying.
Scottish Conservative leader Douglas Ross said he believes Scotland is "lagging behind" other parts of the UK on vaccine rollout and the targets will not be met if the programme does not speed up.
Mr Ross said the number of people vaccinated on Thursday was actually 1,500 fewer than the day before.
"Per head of population Scotland is vaccinating less people than the rest of the United Kingdom," he said.
"We know it is not a supply issue, we know there are adequate supplies of the vaccine, and we hear from the BMA and GPs that they are crying out for these vaccines.
"They are ready to go and they want to by-pass all this bureaucracy and get the vaccines to them. They are desperate to get involved in this programme and they are being held back at the moment."
'Several more weeks'
Public health expert professor Linda Bauld said "good progress" was being made in tackling the virus in Scotland - but that it was "slow progress".
She said: "The situation is still very tricky and it means that the restrictions we have in place, while they are working, are going to continue to be needed."
Prof Bauld predicted that the restrictions would be required for the whole of February.
"I think it is going to take several more weeks until we can actively consider substantially easing restrictions," she said.
She added that large events might be "too risky" this year, and predicted that there would be more cancellations.
Ms Sturgeon said there was "no certainty" about what would happen in the summer with major events such as the TRNSMT music festival.
On Thursday, the Glastonbury festival was cancelled for the second year running due to the Covid pandemic.
Ms Sturgeon was asked if she thought big Scottish live events would go ahead.
She said that the vaccination programme would be well under way, but it would not create a "back to normal environment" by the summer.
"I hope, just like everyone else hopes, that by then we will have restored a lot of normality to life - but we equally have to be realistic and pragmatic," Ms Sturgeon said.
"I think it is going to be a little while longer before big scale events become possible again.
"I hope it is going to be as quickly as possible but is it going to be by the summer? I could not say that with any certainty."