The country recorded 160 new coronavirus infections in the last 24 hours. The total is the highest since May 16 and up from 123 announced on Sunday.
The First Minister said she feels “a greater sense of anxiety today” than at any time “probably for the last couple of months”.
The 160 new cases take the total number since the start of the coronavirus pandemic to 20,478. The death toll remains at 2,494.
Speaking during Scotland’s daily coronavirus briefing, Ms Sturgeon said the spike in infections was “partly a result of greater numbers of people being tested”.
She added that the proportion of people testing positive was still below one percent.
The SNP leader said: “The number of cases we are seeing right now is a reminder to all of us the virus is still a very real risk, it is a development that concerns me and it is one we are taking very seriously.
“We mustn’t lose sight of how important it is if we are to keep schools open, build economic recovery and retain a bit more normality in our lives that we do continue to suppress the virus and push as close to elimination of it as we possibly can.”
Some 69 of the new cases are in the Greater Glasgow and Clyde health board area, while 27 are in Lanarkshire.
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A cluster in Hawick in the Scottish borders had increased to 15 people, she added, with a mobile testing unit in place in the town.
And there are now 188 cases linked to the 2 Sisters food processing plant in Coupar Angus, she said.
The latest easing of Scotland’s lockdown came on Monday with the reopening of gyms, indoor swimming pools and youth groups such as Cubs, Brownies and mother and baby groups.
The First Minister said: “The reopening is a further welcome step in getting back to normal, it is important for wider health and wellbeing.
“But it also obviously brings risks, there is no getting away from that, and that is why we have delayed this until now.
“The figures we are seeing just now for new cases demonstrate very clearly that this virus is still present across the country, it will spread rapidly if it gets the chance.”
Ms Sturgeon warned coronavirus was still “immensely dangerous for some people” and urged the public to “continue to make sure you are not doing anything that gives the virus the chance to spread”.
And the First Minister asked people to “think very carefully about how you’re living your life at the moment”.
She said: “There have been some really dark moments along the way since the start of March and, more recently, there have been moments of greater hope and optimism.
“I have always tried to be frank with you about my assessments and feelings about the situation that we are in, which is why I feel able to say to you today – and feel that it is important I say to you – that I feel a greater sense of anxiety today than I have done any time probably for the last couple of months.
“We are in a fragile position; we have substantially lifted the lockdown restrictions but in doing so we’ve allowed this virus opportunities to spread.”