The latest statistics for the 24 hours to Friday also showed the death toll of people who first tested positive for the virus within the previous 28 days now stands at 9,103, after a further four people died.
The number of deaths now stands at 167 per 100,000 Scots.
National clinical director, Professor Jason Leitch, admitted that as no country had yet found a definitive way to end the spread of the virus, Scotland could be trapped in a cycle of outbreaks and restrictions indefinitely.
According to the statistics, the continued rise in cases has seen a total of 479 people now in hospital with recently confirmed Covid-19, up 53 on the previous day and 167 more than than last week, with 47 patients in intensive care.
Speaking during a Scottish Government briefing on Friday, Ms Sturgeon said there were a record number of tests carried out on Thursday and the daily test positivity rate is 14.2 per cent, up from 11.5 per cent the previous day.
However, she said while the “surge in cases” was not to be ignored, and nothing could be “ruled out”, she again stressed the government did not want to go “backwards” and implement even “limited restrictions”.
She said speculation that a “circuit breaker” – a short, sharp lockdown – could be implemented was not being “currently considered” and urged businesses to ensure they were encouraging customers to comply with mitigations such as face coverings indoors.
“I do not want to go back to restrictions,” she said.
"I hope we can get through this with all of us behaving sensible and appropriately. We are not looking at options right now for a circuit breaker lockdown. If we ever do feel we have to introduce anything, we do that in as limited and as proportionate way as possible.”
She said the Scottish Government was closing monitoring any rise in serious illnesses and "people being hospitalised".
"In the past seven days we have reported more new cases than at any previous time in the pandemic, although I refer back to my point about higher levels of testing, but case numbers have roughly doubled over the course of the past seven days,” she said.
"It's important to point out that case numbers are rising across the UK just now, but after a period of slower increases in Scotland the rise here is particularly sharp at the moment. That is possibly, at least in part, a reflection of the fact that our schools return earlier, with the increased interactions that come with that."
She said the vaccination programme had "significantly weakened", but not "completely broken" the link between cases and serious illness and urged everyone to do their part to help slow the spread of the virus.
"For the moment I do need to stress the vital importance of everyone playing their part in limiting spread of the virus,” she said.
"The more we all do this, the more chance we have of avoiding the need for the re-imposition of any formal restrictions.”
Asked what the route of the pandemic was if, despite vaccinations, cases were rising and if Scotland was in a cycle of rising cases and restrictions, she added: “I don’t know the answer to that question definitively. Vaccines have introduced much more normality, there are few restrictions on our lives now.
“While we were confident vaccines would reduce the chances of people becoming seriously ill and we see that is the case, there was less certainty about transmission – they will reduce your chance of getting the virus, but not eliminate it.
"They’re not a magic wand, but they have delivered so much benefit and it’s unthinkable we would be in the position we are now without them.
“But the virus is still circulating, it’s mutating, so we can’t say for sure right now ‘here’s a date in the future when I won’t be saying to people wear a face covering wash your hands’ … even if Scotland gets to that point we have to be mindful it’s still circulating in the rest of the world.”
Prof Leitch added: “We don’t know the answer, the WHO [World Health Organisation] doesn’t know.
"New South Wales [in Australia] and New Zealand have just locked down again. No country in the world knows how to deal definitively with the ups and downs of this virus. The journey is much harder because of the Delta variant.”
Responding to Ms Sturgeon’s statements, Scottish Labour leader Anas Sarwar said the surge in cases had been “avoidable” and alleged Scotland was unprepared if cases continue to worsen.
“Our NHS remains at breaking point as it does the vital work to catch up on treatments delayed from the last pandemic,” he said.
“That is why any rise in cases that increases pressure is so concerning. And despite this the Scottish Government are still cutting corners on Test and Protect.”
He added: “It is now more important than ever that the vaccination scheme is pushed ahead at pace. The First Minister is right to raise the need to look urgently at the vaccination of 12 to 17-year-olds and how that can be done in Scotland as has happened elsewhere.
“Now is the time for ministers to begin a door-to-door scheme to ensure that the vaccine is being taken up. And there is still a need for consistency in communicating how and why certain decisions are being made.
“But what is now more important than ever is we must have a Test and Protect scheme fit for purpose or risk losing our hard won progress.
“The Scottish Government needs to get a grip of these issues before even contemplating more restrictions. Lockdowns should be our very last resort – not a fall-back option for government incompetence.”
And Conservative Covid recovery spokesman Murdo Fraser said: “Nicola Sturgeon cannot put Scotland’s recovery in jeopardy by heightening the threat of restrictions when our vaccine system has been so successful.
“The Scottish Fiscal Commission are reporting that Scotland’s economy is on course to rebound strongly, earlier than anticipated, with the condition that we keep moving forward past Covid restrictions.
“The SNP Government need to put recovery as the priority over clinging onto powers which, at this stage, are not justified.
“Imposing strict restrictions would have serious consequences for jobs, mental and physical health. Depending on their severity, it may increase NHS backlogs.
The Scottish people cannot be kept in this holding pattern of removing and introducing Covid restrictions, particularly when there is no threat of a new variant at this time.
“The recovery of our NHS and Scotland’s economy is at stake. The SNP must give that more consideration now that so many people have been vaccinated.”