The statistics body said 4.2 million people had been given at least one vaccine dose as of September 30.
A total of 11,262 people have now died in Scotland with confirmed or suspected coronavirus, it added.
The latest data shows 126 fatalities which mentioned Covid-19 on the death certificate were registered in the week October 4-10, a decrease of 17 on the previous week.
This drop marks the second consecutive week where deaths have reduced.
Of those deaths, 26 were of people aged under 65, 24 were people aged 65-74 and 76 were of people aged 75 or over.
The majority – 98 – were in hospital, 19 were in care homes and nine were at home or a non-institutional setting.
Glasgow was the council area with the highest number of coronavirus-linked deaths in that period, at 14, followed by West Dunbartonshire at 10 and West Lothian at nine.
Pete Whitehouse, NRS statistical service director, said: “The latest figures show that last week there were 126 deaths where Covid-19 was mentioned on the death certificate. This is 17 fewer deaths than last week.
“With 1,353 deaths from all causes this week, this is now the 20th consecutive week with excess deaths above the five-year average and is the highest level of excess deaths – 315 this week – since week one (4 – 10 January) of 2021.”
The number of deaths from all causes registered in Scotland in the week October 4-10 was 1,353 – 315, or 30%, more than the five-year average.
Cancer accounted for the highest number of these “excess” deaths at 44, followed by circulatory reasons at 40 and 27 from dementia/Alzheimer’s.
A total of 149 were at home or in non-institutional settings, which was 52% above the 2015-2019 average.
Excess deaths were in hospitals were a fifth above average, at 104, while, those in care homes were around a quarter (26%) above the average at 60.