Figures released by National Records of Scotland showed that the virus had been mentioned on the death certificate of 5,135 people by last Sunday.
This included 278 people who had died in the previous week.
Scotland announced its first confirmed coronavirus death - an elderly patient in Lothian with underlying health conditions - on 14 March
The 278 Covid-linked deaths recorded in Scotland in the week from 9 to 15 November was an increase of 71 from the previous week.
The majority of deaths - 94 - were people over the age of 75, although there were 33 deaths of people aged under 65.
There were 105 deaths in the Greater Glasgow and Clyde health board area, 63 in NHS Lanarkshire and 31 in NHS Lothian.
Most were in hospitals (198 deaths), with 72 deaths in care homes and eight at home or in non-institutional settings.
Last week, the UK as a whole became the first country in Europe to have seen more than 50,000 people die within 28 days of testing positive for the virus.
The number of people in Scotland to have died by this measure currently stands at 3,377.
Speaking at her daily coronavirus briefing, First Minister Nicola Sturgeon said the statistics were "grim and distressing".
She added: "When we are through this pandemic we will want to consider how, as a country, we commemorate the lives that virus has taken."
Highlighting more positive news about the Pfizer vaccine, which suggests it is 94% effective in people over the age of 65, Ms Sturgeon said that an end to pandemic was starting to appear on the horizon.
The first minister said: "One of the things we should be focused on now, and all try to play our part in, is how we get to the end of this with as few additional lost lives as possible."