The figures show eight deaths were registered that mentioned Covid-19 on the death certificate in the week of May 24-30 – an increase of four deaths from the previous week.
Two deaths were in people aged under 65, one was in the 65-74 age group and five were people aged 75 or over.
There were two deaths in North Lanarkshire and two in Glasgow City, while South Lanarkshire, the Western Isles, Falkirk and East Ayrshire each recorded one death.
Six deaths were in hospitals and two were at home or in a non-institutional setting, while there were no care home deaths involving Covid-19.
The statistics are published weekly and cover all deaths registered in Scotland where Covid-19 was mentioned on the death certificate.
They differ from the lab-confirmed coronavirus deaths announced daily by the Scottish Government because the NRS figures include suspected or probable cases of Covid-19.
Pete Whitehouse, NRS director of statistical services, said: “The latest figures show a slight increase in deaths where Covid-19 was mentioned on the death certificate, although numbers remain at very low levels.
“There were six Covid-19 related deaths in hospitals, none in care homes and two elsewhere.”
Three of those who died were female and five were male.
The number of deaths from all causes registered in Scotland over the week was 1,084 which was 39 deaths more than the five-year average.