The rate of cases has also declined in Midlothian.
The results come as Scotland recorded the highest daily total of cases in more than a month, at 394.
Daily positive cases have not reached above 400 in Scotland since the beginning of April.
Test positivity across the country is still relatively low, however, at 1.6 per cent.
Glasgow and Moray are in level three restrictions due to high case numbers, with a review of the situation due at the end of the week.
The Scottish Government will also review whether to place any other areas in local restrictions, with East Renfrewshire and Midlothian highlighted as those most at risk.
The rate of cases per 100,000 people in Glasgow has risen to 110, up from 80 on Friday, when the decision was made to keep the area in level three.
The most affected areas are in the south of the city, around Pollokshields, Darnley and Maxwell Park, and Govanhill.
NHS Grampian has said it is pleased with progress in Moray, with high uptake of extra testing and vaccination for all those over 18.
NHS Greater Glasgow and Clyde began a programme of door-to-door PCR testing in the most affected area of Pollokshields.
Around 10,000 tests will be offered by nurses, contractors and British Red Cross volunteers.
Lateral flow testing kits will also be delivered to all households in the G41 and G42 postcodes.
The rate in neighbouring East Renfrewshire, which has become the area with the second-highest figure, has risen to 102.
The outbreak here is centred around Merrylee and Braidbar as well as Mearnskirk and South Kirkhill.
Midlothian has the third-highest rate of cases, but the figure has dropped slightly to 56.
In Moray the figure has dropped from 69 on Friday to 41.
Across the whole of Scotland the rate per 100,000 people is 36.
Deputy First Minister John Swinney announced on Tuesday that alongside a review on Friday of whether or not Glasgow and Moray will be able to leave local restrictions, there will also be a review of whether any other areas will have restrictions tightened.