Those over 55, along with anyone in previous JCVI priority groups who have not yet received a vaccine, have been asked to arrange an appointment themselves if they have not yet been offered one.
Earlier this week the Western Isles became the first health board to vaccinate half its adult population at just over 11,000 people.
NHS Western Isles Chief Executive Gordon Jamieson said the area had enjoyed a “very high uptake” of the vaccine.
“We have now vaccinated 50.4 per cent of all adults (11,316 individuals in total) in the Western Isles, which is the highest vaccination rate in Scotland,” he said on Tuesday. “We are also progressing well with second vaccinations, and over 700 second doses have already been administered. “We continue to make excellent progress but the speed at which we can offer appointments in dependent on the vaccine supplied to us, so we would ask for your patience as we continue with this very important programme.”
As of Wednesday, NHS Shetland boasted the second-fastest vaccination rate at 49 per cent, followed by Dumfries and Galloway.
NHS Lothian has continued to have the slowest vaccination rate throughout much of the programme, and now stands at 32 per cent of adults.
Some 34 per cent of those in NHS Grampian and Glasgow and Clyde have received a first dose.
Some of those in older age groups are still waiting for vaccinations despite their cohort having been passed.
Fife-based military veteran John Hamilton, 75, said he and his wife, 70, had tried “every avenue they could think of” to try and register for a vaccine appointment.
After almost a month of calls to his local GP practice, calls to the national vaccination helpline and emails to local MSPs and Health Secretary Jeane Freeman, the couple were eventually vaccinated on Friday afternoon.
“I find it a shame that a person 70 years of age, and a career military officer can not make a simple call to an agency, provide them with our NHS and CHI numbers and get a simple appointment date set to receive a vaccination,” he said.
Health Secretary Jeane Freeman said on Wednesday that vaccination is continuing for some people in priority groups which have already been declared complete.
She said: “We continue to reach people, and we continue to have people come forward who may feel that they have been missed, contacting our national vaccination line or their GP practice,” she said.
"Where that actually is the case then we – please don’t take it as disrespectful – we mop those up.
"That is a feature of vaccination programmes, it’s a feature of our flu vaccination programme, and a feature of all vaccination programmes.
"We are really determined to reach every single adult over the age of 18 as quickly as we can.”
Those eligible for a Covid-19 vaccine in the Western Isles are invited to call 0808 196 8383.