A total of 56,676 people in Scotland have received their first dose of the Covid-19 vaccine, the health secretary told Holyrood, with plans for those people to have their second jab by the end of January.
That number includes care home residents, care home staff, and patient-facing NHS staff, Ms Freeman added.
The health secretary added that NHS Scotland expects to receive an additional 172,575 doses of the Pfizer vaccine by the end of the week, half of which will be retained to ensure people get their second dose.
Ms Freeman added that pending the approval of the AstraZeneca vaccine by the Medicines and Healthcare products Regulatory Agency (MHRA), the Scottish Government plans to begin the rollout of that vaccine to over-80s who do not live in care homes across Scotland.
She said these jabs were most likely to be administered in GP practices.
The health secretary said: “A key area that would help streamline the process further is predictability of delivery but this is not in our gift.
"Safety is a paramount concern and there is a rigorous process of safety checks between the vaccine leaving the factory in Belgium and arriving in the UK and then arriving in Scotland.
"These checks mean that while we know when the vaccine leaves the factory, we cannot be certain of the date we will receive it.
"This is a challenge for our forward planning of vaccine appointments but it is one shared across all four nations of the UK and we are working together to resolve this with the regulator and the distributor.”
Regulatory approval of the AstraZeneca vaccine is viewed as being crucial in the attempts to vaccinated everybody on the Joint Committee on Vaccination and Immunisation’s (JCVI) priority list by Spring.
Once those groups have been vaccinated, the programme will move to vaccinate the rest of the population.
Ms Freeman added that terminally ill patients who are hoping to get access to the vaccine will have to wait for further regulatory decisions with both the UK and Scottish Governments writing to the JCVI asking for additional clarity.
She added the use of large city-based vaccination centres are being examined for the potential rollout of the vaccine in Glasgow, Edinburgh, Dundee, Aberdeen and Lanarkshire alongside mobile sites to be used in rural areas.
The health secretary added that the NHS has access to 1,729 registered vaccinators with 4,000 attending training events on the delivery of the Pfizer vaccine.
Ms Freeman said workload requirements estimate a need for 1,400 vaccinators and 600 support workers to hit the target of Spring for the JCVI priority list, saying the Scottish Government “remain confident” in their workload supply.
She said: “A vaccination programme of this scale is unprecedented and it is a significant logistical challenge requiring a major nationwide effort.
"It is a challenge that we continue to take with optimism and determination to succeed for Scotland.”
The health secretary also gave an update on the testing programme, saying plans to set up in-school testing in pilot schemes in January.
Community-based testing of asymptomatic people will also be extended after success in areas such as Johnstone.