John Swinney has warned further restrictions may be applied to East Renfrewshire after a rise in coronavirus cases.
The Deputy First Minister admitted the rise in covid cases in the area on the outskirts of Glasgow have been "very swift".
He added that the situation was being monitored by the Scottish Government.
It comes as cases in the area overtook Moray to 75.4 per 100,000 population, according to the latest seven-day average figures.
The city of Glasgow currently sits at 94.5 cases which breaches the 50 cases per 100,000 benchmark for moving down to Level Two lockdown restrictions.
Moray and Glasgow are the only parts of mainland Scotland not moving down to Level Two restrictions today due to the high level of infections.
Scotland's island communities have shifted down to Level One.
Speaking on the BBC's Good Morning Scotland, Swinney said: "The East Renfrewshire rise has been very swift in taking its course. We will continue to monitor the situation in every local authority area and we look at every single outbreak and determine whether there is further patterns that are emerging from these particular outbreaks.
"If there is a necessity to take action to apply restrictions once again we will unfortunately have to do that.
"We made it very clear, as we set out the basis of moving from Level Three to Level Two that there may be circumstances where we have to apply further restrictions to make sure that we contain any outbreaks that take place.
"We will continue to monitor that every day."
On the more general picture across the country, he said: "I think there is obviously grounds for a lot of optimism and the relaxation of restrictions enables people to get on with more and more of their lives.
"But the situation that we face in Glasgow and in Moray illustrates just how fragile the progress that we are making is - so I suppose what I would say to members of the public is that we need to continue to tread carefully and cautiously and wearily as we relax these restrictions.
"As we enjoy some of the freedoms that we now have, we've got to handle them with a great deal of care."
When asked about lifting restrictions earlier in Moray, he added: "I doubt it could come earlier but we will certainly review it as we promised we would do in the course of this week and we'll continue to look at other situations around the country.
"The last thing we want to do is to have local authority areas going in and out of restrictions like a yo-yo, that's the worst of all possible models for the business community and the wider community.
"Obviously we're still facing quite an acute problem in Glasgow, we've got a great deal of testing infrastructure that's been deployed."
