Glasgow is the only part of Scotland to remain at a higher tier of coronavirus restrictions after Nicola Sturgeon announced the Moray council area will drop to Level 2.
Speaking at a Scottish Government coronavirus briefing on Friday, the First Minister said Glasgow will remain at Level 3 for a further week before review.
She said improvements following measures brought in to tackle an outbreak in Moray mean it can drop to Level 2 from midnight on Friday.
East Renfrewshire, which has a higher seven-day average rate of cases per 100,000 people at 118.3 than Glasgow, will remain in Level 2.
In Level 2, people can hug and meet indoors – subject to restrictions – and hospitality venues can open later than in Level 3 and serve alcohol indoors.
Ms Sturgeon said the total number of cases in East Renfrewshire is significantly smaller than in Glasgow, with only 17 on Thursday compared to 166 in the city.
Speaking about the situation in the Glasgow City Council area, Ms Sturgeon said there had been “extensive public health measures” deployed over the past 10 days.
This includes enhanced testing and vaccination in the areas with the highest rates of coronavirus, particularly in the G41 and G42 postcodes.
But the First Minister said: “Despite all the efforts that have been made in the past 10 days, cases are still rising in Glasgow.”
She added authorities are “fairly certain” the increase is being driven by the Indian variant of the virus.
The First Minister said the number of cases per 100,000 population in Glasgow had gone from 71 last week to 112 now.
The percentage of tests coming back positive in Glasgow has also increased over the last week from 3.1% to 4%, she added.
“We don’t think we have turned the corner in Glasgow yet,” Ms Sturgeon said.
Ms Sturgeon said she was “confident” the measures put in place in Glasgow will bring the outbreak there under control but needed a “bit longer to do that”.
She added: “I genuinely hope it will not be for too much longer.”
Cases in East Renfrewshire could be traced to “specific household clusters”, she said, but in Glasgow “transmission appears to be much more widespread”.
In Moray – which like Glasgow had stayed in Level 3 when the rest of mainland Scotland moved to Level 2 at the start of this week – the “situation has improved very significantly”, Ms Sturgeon said.
She said infection levels were down from 98 new cases a week per 100,000 people last week, to 37, with test positivity falling from 2.8% to 1.3%.
She also gave an update on the daily coronavirus figures in Scotland.
Across the country 414 new coronavirus cases but no deaths were recorded in the past 24 hours, the First Minister said.
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.
The daily test positivity rate was 1.9%, up from 1.6% the previous day.
There were 81 people in hospital on Thursday with recently confirmed Covid-19, down two from the previous day, and of these four people were in intensive care, down one from the day before.
So far 3,820,251 people in Scotland have received the first dose of a Covid-19 vaccination.
Meanwhile, the latest figures from the Office of National Statistics indicate around one in 1,960 people is estimated to have had Covid-19 in the week to May 15, compared to one in 1,250 in the previous week.
This is the lowest since estimates began for Scotland in October.