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NRS data also shows there have now been nine people in Scotland whose underlying cause of death was due to the adverse effects of vaccination against Covid-19.
In addition, a further two deaths where an adverse effect was mentioned on the death certificate were also recorded.
By the end of February separate statistics from Public Health Scotland showed that 4.4 million Scots have had at least one dose of coronavirus vaccine.
The overall death toll published by NRS covers all cases in Scotland where Covid-19 was mentioned on the death certificate.
This differs from the lab-confirmed coronavirus deaths announced daily by the Scottish Government because the NRS figures include suspected or probable cases.
Pete Whitehouse, director of statistical services at NRS, said: "The latest figures show that last week there were 117 deaths where Covid-19 was mentioned on the death certificate.
"This is six more deaths than the previous week."
He added that for the week ending March 13 the overall number of deaths registered from all causes was 1,207 - 1% less than the five-year average for the period.
The latest weekly figures showed there were 14 coronavirus deaths in both Edinburgh and Glasgow, as well as 11 in the Highland Council area.
Across Scotland, 27 of the 32 council areas had at least one death involving Covid-19 last week.
The majority of deaths - 74 - were in hospitals, with 36 in care homes and seven at home or in a non-institutional setting.
Of those who died, 90 were aged 75 or above, 17 were 65-74, and 10 were under the age of 65.
The news comes as it was revealed that more than 27,000 doses of Covid vaccine were thrown away in Scotland in February, at a wastage rate over eight times the average across the previous five months.