There is evidence the rate of case growth may have slowed since Tuesday last week, Ms Sturgeon said, although she warned that it was “early days”.
Case numbers by specimen date peaked on that day, she said, at around 3,200 positive tests.
The latest case numbers showed that 3,118 more people had been diagnosed with coronavirus since Monday, while one more person has died.
Ms Sturgeon said: "This is early days and we need to monitor this over the course of the coming days. But when we look at cases over the past week by the date the specimen was taken, as opposed to the date on which we reported the test result – which are the numbers we report on a daily basis – then what we see is a peak in cases last Tuesday.
"And since then, we have seen what appears to be a swing down of the rate of increase. So that's encouraging. But again, I would stress that it is early days.”
She added: “Obviously last Tuesday, we were worried it would keep rising like that. But that rate of increase appears to have marginally slowed.”
She said the Scottish Government would continue to publish case numbers for the foreseeable future, despite the link being “broken” between high case numbers and hospitalisations and deaths.
Ms Sturgeon said: “We are seeing less of a focus on case numbers than we were earlier in the year.
"We would never have tolerated these numbers at this level without strict measures earlier in the year because we had no vaccine protection. We are not in lockdown now.
"We've got relatively few restrictions still in place. So if it wasn't for the vaccine, the 3,000 or thereabout, cases that we're reporting right now, with no restrictions in place that would probably be several times that.
"So the context has already changed, because we are not seeing that link between cases and serious illnesses. But it’s not completely broken and it might never be completely broken.
"The information that we're looking at today, we won't necessarily take the same action as we would on the back of the same information six months ago, because vaccination has really changed the game.”
Ms Sturgeon said Scotland s Covid case figures had generally been behind those of England and Wales throughout the pandemic, leaving people with fewer antibodies to the virus, which was fuelling the third wave.
She said: “Definitively in the first two waves of this virus, Scotland was a bit behind and below the curve in other parts of the UK, although we were all following the same pattern.
"In this third wave because I think that's pretty much what is now unfolding across the UK, we are slightly ahead and above at this stage. I would imagine that we may see that change over the next couple of weeks, depending on how things unfold in England and other parts of the UK, but that's where we are just now.”
She said the Delta variant had seeded first in Scotland in Glasgow – the country’s biggest city – which had given it more scope to spread.