They have reported that the total number of deaths registered between April 26 to May 2 was 19, the lowest number per week since September.
The data from the National Records of Scotland differs from that of the Scottish Government as they include all deaths where coronavirus is mentioned on the death certificate.
NRS also reported that 79% of the deaths were people aged over 75, with 11% under the age of 65.
53% were male and 47% female.
It brings the total number of fatalities up to Sunday to 10,097.
Twenty of the country’s 32 local authorities did not record a death involving Covid-19 in that week.
Eight deaths were in the Greater Glasgow and Clyde Health Board and three in Lanarkshire.
Two deaths were in each of Ayrshire and Arran, Forth Valley and Grampian.
58% of deaths occurred in hospitals, with seven in care homes and one death at home or in a non-institutional setting.
Pete Whitehouse, director of statistical services at NRS, said: “We continue to see a progressive decline in the number of deaths involving Covid-19 since January and while that trend is very welcome, I am mindful that each represents a painful loss for a family in Scotland.
“There were 1,035 deaths in total from all causes this week, 5% lower than the five-year average.”