The First Minister said almost a third of adults in Scotland have now been given their first dose of the vaccine.
Experts found those who have had their first dose reduced their risk of hospitalisation by up to 94%.
The Scottish Government is moving to its next phase in the vaccine rollout.
The NHS is asking people not to turn up at vaccination centres without an appointment.
The Scottish Government will now send out white, windowed envelopes after a supply issue for blue ones.
The 'distinctive' blue envelopes have been given priority by Royal Mail and will start arriving through letterboxes from Monday.
Professor Leitch made the comments as Covid-19 vaccines are scaled up around the country,
The Oxford University/AstraZeneca vaccine has become the latest coronavirus jab approved for use in the UK.
Jab given the green light by the Medicines and Healthcare products Regulatory Agency following clinical trials.
The Pfizer/BioNTech jab will begin to be distributed across Scotland from Tuesday.