The number of deaths in the week to July 3 was 61 – up from 52 in the previous week.
Coronavirus deaths have risen for four consecutive weeks, according to the NRS data.
The figures were released as it was announced that that a Holyrood committee is to analyse the impact of the pandemic on the labour market in Scotland.
MSPs on the Covid-19 Recovery Committee are to consider how issues such as long Covid, and other long-term illnesses, have impacted the number of people in work.
The inquiry comes as economic experts have raised concerns about the number of people who are no longer part of the workforce, and are classed as “economically inactive” – such as students and those who have retired.
The Fraser of Allander Institute has already reported that the number of Scots in this group has increased by more than 20,000 since before the pandemic.
Committee convener Siobhian Brown said: “Unlike previous economic shocks, where the labour force numbers recovered much more quickly, we are seeing concerning persistent numbers of long-term economically inactive people.
“We want to find out why this has happened and what needs to be done to encourage these people back into the workplace.
“We are keen to learn more about the labour market impact of the pandemic on people with pre-existing health conditions, what influenced people to take early retirement and whether specific groups of society or areas of the country have been impacted more than others.
“There is no doubt that the reasons behind this will be complex but in order to address this issue we must first understand why people are no longer working.”