The figures from Public Health Scotland show the rolling seven-day average to Friday May 14.
This rate is rising in Glasgow which has the highest such rate in Scotland at 100.3 per 100,000 amid an outbreak in the city.
East Renfrewshire is also increasing and has a rate of 86.9 per 100,000, higher than the Glasgow’s when it was announced on Friday the city would be kept in Level 3 restrictions.
This rate is also rising in Midlothian and is 55.2, having more than doubled in a week.
In Moray, the rolling, seven-day average rate of cases per 100,000 was 59.5 as of Friday, down from a peak for the current outbreak of 100.2 recorded on May 9.
Moray and Glasgow are the only two council areas in mainland Scotland remaining in Level 3 restrictions as the rest moved to Level 2 on Monday.
Many island areas have very low case rates and have moved to Level 1.
NHS Grampian accelerated its vaccination programme in Moray to tackle the outbreak.
In Glasgow, people aged 18-39 in the worst affected neighbourhoods are being offered coronavirus vaccinations.
NHS Greater Glasgow and Clyde (NHSGGC) said it is targeted the following areas in the city: Battlefield, Gorbals and Hutchesontown, Govanhill, Aikenhead, Kingston West and Dumbreck, Maxwell Park, Mosspark, Pollokshields and Strathbungo.
These include the G41, G42, G5, G51 and G52 postcodes.
The health board also plans to bring forward second doses for those aged 50 and over in the worst-hit areas.
NHSGGC said in a statement: “We are actively pursuing ways to ensure vaccination uptake is as high as possible in the areas with the largest increases of cases.
“This will include encouraging and supporting people who previously opted not to receive their vaccination to arrange an appointment. We will be contacting these individuals directly and offering them appointments in the coming weeks.
We would like to encourage all residents of Greater Glasgow and Clyde to continue to follow Scottish Government guidelines, take your vaccination when offered and make use of our asymptomatic testing facilities to ensure if you unknowingly have the virus, you can then self-isolate and help to stop the spread.”
Meanwhile, the latest daily figures for Scotland indicate 161 new coronavirus cases have been recorded in the past 24 hours.
No new deaths have been recorded meaning the death toll under this daily measure, of people who first tested positive for the virus within the previous 28 days, remains at 7,664.
A total of 229,774 people have tested positive for the virus and the daily test positivity rate is 1.6%, down from 2% the previous day.
A total of 68 people were in hospital on Sunday with recently confirmed Covid-19, with three patients in intensive care.
So far, 3,035,790 people have received the first dose of a Covid-19 vaccination and 1,638,536 have received their second dose.