New Covid cases have more than doubled in the past week, with the worst ever number of cases recorded in one day posted on Tuesday, and with almost half being diagnosed in people under the age of 25.
Ms Sturgeon said she could not “completely rule out” reimposing coronavirus restrictions as a result of "one of the sharpest rises we have experienced at any point during the pandemic". The spike has led to hospital and intensive care cases also increasing.
However, in a move to ease parents’ concerns, the First Minister said top of the list “of things I don’t want to see going backwards” was the opening of schools. She reiterated that she hoped vaccinations could soon be offered to those under 16.
But Scottish Conservative Leader Douglas Ross labelled the lingering threat of fresh restrictions as “unjustifiable”, claiming the First Minister was “unable or unwilling” to give up control.
Scotland recorded ten coronavirus-linked deaths and 4,323 cases in the 24 hours to Tuesday.
Speaking at a Scottish Government coronavirus briefing in Edinburgh, Ms Sturgeon said the daily case figure was "the largest we have ever recorded in a single day", but highlighted more testing was now taking place than in the early stages of the pandemic.
She warned Scotland was now at a "fragile and potentially pivotal moment" in the fight against the virus as vaccinations had weakened the link between cases and serious harm, but not completely broken it.
"That means the rise in cases in the last week may well result in more people having to go to hospital in the coming days, perhaps requiring intensive care treatment, and, unfortunately, a rise in cases like this will still lead to an increase in numbers of people dying,” she said.
"That also means that, if this surge continues, and if it accelerates and if we start to see evidence of a substantial increase in serious illness as a result, we cannot completely rule out having to reimpose some restrictions.
"Of course, we hope not to have to do that and, if we did, we would be as limited and as proportionate as possible.
"However, as has been the case throughout so far, and up until this point, what happens in the next few weeks will depend, to a large extent, on all of us."
Ms Sturgeon added: "We always knew cases were likely to rise as restrictions eased, so to some extent what we are seeing now is not entirely unexpected.
"That said the scale of the increase is still a cause of real concern."
The First Minister urged people to adhere to the remaining restrictions, such as wearing face coverings in indoor public areas, as well as regularly taking lateral flow tests and getting fully vaccinated if they had not already.
Asked if there could be a return to home-learning, which had been raised by government adviser Professor Linda Bauld, who was concerned a fresh spike in cases could lead to pressure for schools to be closed, the First Minister said: "Schools are not suddenly going to be closed again.
"Right at the top of the list of things I do not want to see going backwards is the ability of children to be at school. I think all of us have a duty to try to limit the spread of the virus so we keep children at school.”
She added that she hoped the Joint Committee on Vaccination and Immunisation would recommend the vaccination of younger cohorts of children, but the government had to wait for its advice.
Chief Medical Officer Gregor Smith said: “We’re keeping a very close eye on all age groups, but if you look at the 0-19 age group we’ve got about 34 per cent of cases announced today falling within that group and the sharpest rise is the 18-19 year old group.
"We will continue to track this and make sure we’re encouraging those people to make sure they’re taking up the opportunity to test on a regular basis before going into schools. At this moment in time there’s no further action necessary in terms of making the schools safer than they are just now.”
Both Dr Smith and Nicola Sturgeon said that Scotland was in a “catch up” phase with the rest of the UK, which was why the nation's cases were rising faster, blaming the difference on the three-week lag between when restrictions were lifted earlier south of the border.
But responding to the warning of restrictions, Mr Ross said: “Nicola Sturgeon’s lingering threat to impose more constraints on people’s lives is unjustifiable, given the success of Scotland and the UK’s vaccine scheme.
“The public want to move on, but Nicola Sturgeon is unable or unwilling to give up the control she has had.
"Just a few weeks after most Covid rules have been dropped, she’s talking of bringing them back. She seems determined to prolong restrictions, no matter the cost to jobs, our NHS or people’s mental health.
“The SNP Government is clinging onto the thought of introducing more restrictions when people across Scotland are fed up with strict Covid controls. They just want to get their lives back to normal.
“Scotland shouldn’t go backwards. This is a different phase of the pandemic, when NHS remobilisation and rebuilding Scotland’s economy should be our top priorities.”
Scottish Liberal Democrat leader Alex Cole-Hamilton described the rising case numbers as "troubling".
He said: "I think it is very telling that was not met with the introduction of further restrictions.
"It suggests we have moved to a different phase in Covid where we have accepted we have to live around it, and it will be a fact of life for the foreseeable future."
Dr Smith said it was important to remember how the virus had evolved over the past 18 months and stressed the Delta variant was “incredibly effective at transmitting from one person to the next”.
“Of course, that has implications for us all because it is much easier for us now to come into contact with people who are perhaps carrying this virus and as a result of that to become a positive case ourselves,” he said.
"We know so much more about Delta now. One of the key things is the high levels of what is called viral shedding, so it's a marker of infectivity.
“The high levels of viral shedding [occur] particularly within the first 48 hours of infection prior to people showing any symptoms.
"And that really is one of the keys as to why this virus is much much more transmissible than previous versions of the virus because it needs much less virus in order to actually infect human cells.
"And it has this period before people show any kind of symptoms, where it’s able to replicate in significant numbers, in nasal passageways and in our throats and be able to spread to others from there.”
He added: "So whether people are vaccinated or not my really strong advice is that we continue to be cautious, we continue to make sure that we're taking the steps to ensure that people round about us don’t get infected if we're carrying the virus, and that we don’t come into contact with others who might as well.
"Simple measures like face coverings, like keeping up distance, like washing your hands regularly can make an enormous difference.”
With vaccination "making a big difference", Ms Sturgeon said many of the new cases were in younger people, who were "less likely" to have had both doses of vaccine.
She said "around half of all new cases right now" were in people under the age of 25.
So far, 4,850,552 people have received the first dose of a Covid-19 vaccination and 3,587,145 have had their second.
Giving a further update on the daily figures, the First Minister said the death toll under the daily measure, of people who first tested positive for the virus within the previous 28 days, was now 8,080.
The daily test positivity rate is 14.5 per cent, up from 12.4 per cent the previous day.
A total of 364 people were in hospital on Monday with recently confirmed Covid-19, up by eight on the previous day, with 43 patients in intensive care, up two.