Universities Scotland director Alastair Sim warned further outbreaks among students remain likely.
Aberdeen co-leader Douglas Lumsden hit back after Nicola Sturgeon accused him of writing her 'ridiculous letters'.
Further infections confirmed at Parker House and Abertay University's Meadowside Hall.
Nicola Sturgeon addressed students after they were banned from pubs and socialising outside their households.
Two deaths involving coronavirus were logged in the week ending September 6, both in hospitals.
There is some Covid-19 transmission in the city's hospitality sector, the First Minister said.
Covid cases in Highlands town Grantown increase by two to 33, with 30 linked to Millers of Speyside slaughterhouse.
There are 31 Covid-19 cases in Grantown-of-Spey, with 29 associated with Millers of Speyside slaughterhouse.
NHS Grampian's incident management team say cluster is finished after three-week lockdown.
People living in Glasgow City, East Renfrewshire and West Dunbartonshire council areas face new restrictions.
Infections have risen at the 2 Sisters factory outbreak in Perthshire, while there are also new cases in Hawick.
From August 31, pupils should be wearing face coverings in areas where physical distancing is not possible.
Scottish pupils have mostly returned to full-time education - except at schools where coronavirus cases crop up.
Nicola Sturgeon said the 'reluctant' decision had been made as the city's outbreak is not 'completely under control'.
There are 16 new cases in Tayside, where an outbreak at a chicken factory has been discovered.
Aberdeen has been in local lockdown for nearly two weeks with 207 cases linked to pubs outbreak.
NHS Grampian says the cases are associated with The Hawthorn Bar in the city centre.
Cases have risen moderately in recent weeks along with testing, but no deaths for 16 days.
A total of 17 employees at the test and trace site in Bellshill have Covid-19 along with seven of their contacts.