Parts of the country will move from level 2 to level 1 of the five tiers of restrictions, which run from 0 to 4, she told the Scottish parliament.
But Edinburgh and Midlothian, Dundee, East Dunbartonshire, Renfrewshire and East Renfrewshire, the three Ayrshire areas, North and South Lanarkshire and Clackmannanshire and Stirling will remain in level 2.
Glasgow, which was kept in level 3 when measures eased in the rest of the country on 17 May, will move to level 2 on Saturday. Sturgeon said the outbreak there had stabilised with case numbers falling slightly. Glaswegians will be able to drink alcohol indoors, meet in private residences and hug loved ones from the weekend.
Those in level 1 areas can meet outside and indoors in public places in larger groups. Numbers at events, weddings and funerals can also increase, and pubs can open slightly later indoors.
Scotland currently has the highest rate of new cases of covid-19 of the four nations of the UK.
But Sturgeon said there are “many parts of mainland Scotland where cases are at very low levels and broadly stable, or where case numbers might appear to be rising, but we are assured that they relate to clusters that are being managed”.
Scottish Conservative leader Douglas Ross previously said areas shouldn’t be left behind if restrictions are relaxed.
“Everyone understands that there will be a need for local, targeted measures when an outbreak occurs,” he said. “But leaving behind whole areas should be ruled out. Sweeping measures that unnecessarily hurt a whole city or council area are unfair on businesses and local people waiting to get on with their lives.”
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