But vaccination rates vary significantly from health board to health board, with some areas having almost completed their first-dose regimen while in others some people over 50 and with underlying health conditions – priority groups which should have been given an appointment four weeks ago – are still waiting.
The Scottish Government was unable to say when all Scots over 40 could expect to be given a first dose.
A spokesperson said supply is the limiting factor in disparity between health boards, and added that rollout in small communities is “very different” to that in cities.
NHS Western Isles became the first health board to open the programme to all adults over 18 at the end of April.
Now more than 86 per cent of over-16s have been given a first dose, while in Shetland that figure is 82 per cent and in Orkney it is 78.
Lothian has remained the slowest health board in terms of population throughout the pandemic, with 56 per cent of its population given a first dose, along with 61 per cent of those in Greater Glasgow and Clyde.
NHS Grampian recently become the second health board to open up vaccination to everyone over 18, but just in Moray, in an urgent bit to combat an escalating Covid outbreak.
Asked whether vaccines could be shared between health boards to speed up the rollout in some areas, the Scottish Government said: “Vaccine doses are being allocated to local health boards on an equitable basis, recognising the different population share and geography.
"The way that the vaccine is rolled out in a small island community is clearly very different to how it is rolled out in our cities. NHS Lothian and NHS Greater Glasgow and Clyde receive their agreed allocation and continue to take forward the vaccination of their populations as quickly as is practicable.”
The ramping up of vaccination in Moray has not had a detrimental effect on other areas of Grampian, as the extra vaccine doses came from national stocks.
The Scottish Government said it holds a “limited national supply” to support health boards needing extra doses.
“It really is supply dependent,” said Jillian Evans, head of health intelligence at NHS Grampian.
"We do operate a kind of mutual arrangement with other health boards, but by and large our sharing of vaccine has been pretty much confined to our own health board.”
While she acknowledged there are differences between rollout speed across boards, Dr Evans added: “Scotland’s approach really is one of mutuality. Apart from in the early days of the vaccination programme when supply was much less assured, by and large at the moment supply has become a little bit more reliable, and most places have been able to cope.”
Variation also continues between Scotland and other UK nations, with around 65 per cent of over-18s given a first dose in Scotland, compared to 67 per cent of those in England, almost 70 per cent in Northern Ireland, and nearly 75 per cent in Wales.