Giving an update on the Covid-19 vaccination programme to the Scottish Parliament on Wednesday, she said the Scottish Government will “do what it takes” to support the vaccination rollout.
She also outlined plans to vaccinate 400,000 Scots a week by the end of February, with mass vaccination sites able to accommodate up to 20,000 people a day.
Responding to a question from Scottish Labour MSP Monica Lennon on when 24-hour vaccinations could begin, the Health Secretary said this will be “entirely possible” at the mass vaccination sites.
In a later briefing, Chief Executive of NHS Scotland and Scottish Government Director General of Health and Social Care Caroline Lamb said NHS Scotland will work with health boards to extend vaccination hours if there is need to do so.
Of the mass vaccination sites, she said: “They will be operating seven days a week. Our current plans are from eight in the morning until eight in the evening, and that is based on the scale up of the amount of vaccine that we'll have available to us.
"If we find that there is demand outwith those hours then we will work with our NHS boards to extend those operating times.”
Dr Nicola Steedman, Interim Deputy Chief Medical Officer, said the aim is for Scots to be able to choose where they would like to receive a vaccine – as not everyone will be able to travel to a mass site.
Ms Freeman announced that as of the end of Tuesday, 191,965 Scots had been given a first dose of the vaccine.
This means 16,023 doses were given on Tuesday, an increase on 12,565 the day before.
Some 2,990 people have received a second dose of the Pfizer vaccine, although the timetable for second doses was changed in the new year from three weeks after the first to up to 12 weeks later.
From the end of February Scotland will have the capacity to vaccination 400,000 people a week, Ms Freeman said.
This will involve 1,700 full-time equivalent vaccinators a day, as well as just under 1,000 support staff.
So far just over 80 percent of care home residents have been given a first dose, along with 55 per cent of care home staff and 52 percent of frontline NHS and social care staff.
By the first week in February, all residents in care homes and staff will have been given a vaccine, along with frontline NHS and social care staff and those 80 and over, Ms Freeman said.
By mid February, those over 70 will have been given a first dose, and the aim is to deliver a dose to all those over 65, and the clinically vulnerable by the beginning of March.
Ms Freeman said Scotland will receive the first deliveries of the Covid-19 vaccine made by Moderna, the third vaccine to be approved in the UK, in early April.