NRS said the deaths are in the context of 3.27 million people who had been given at least one vaccine dose by May 31, according to statistics from Public Health Scotland.
The latest figures also show 10,137 people have died in Scotland with confirmed or suspected coronavirus.
Seven fatalities which mentioned Covid-19 on the death certificate were registered in the week to June 13, one fewer than the previous week.
Of the deaths in the week to June 13, five were people aged 75 or older, while the remaining two were between 65 and 74.
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.
The NRS report also said that Scotland’s Covid-19 death rate fell close to its lowest level in May.
Accounting for age and population structure, six in every 100,000 people died from Covid in May, while the lowest monthly rate was four per 100,000 in August 2020.
The figures show those living in the most deprived areas are more likely to die with Covid than those in the least deprived places.
Pete Whitehouse, NRS director of statistical services, said: “The latest figures show that last week there were seven deaths where Covid-19 was mentioned on the death certificate.
“After adjusting for age, people living in the most deprived areas were 2.4 times as likely to die with Covid as those in least deprived areas.
“The size of this gap has slowly widened from 2.1 to 2.4 over the course of the pandemic.”
Over the period of the pandemic from March 2020 to May 2021, 186 males per 100,000 people died with Covid-19 mentioned on their death certificates, compared with 128 females.