Nearly 17,500 children were tested for coronavirus across Scotland over the past week - but only 49 were positive, Nicola Sturgeon has said.
Demand for testing has increased "significantly" since pupils returned to schools earlier this month
But the first minister said the 49 children aged between two and 17 who tested positive last week was only two more than the previous week.
This was despite a 300% increase in the number of children who were tested.
Ms Sturgeon said this underlined that parents and teachers should not be "unduly concerned" about the return to school.
The total number of people who have tested positive for coronavirus in Scotland has now passed 20,000, with a further 68 positive results over the past 24 hours.
A huge rise in demand for coronavirus tests has seen some people in Scotland told they must travel hundreds of miles - including to England and Northern Ireland - to attend a testing centre.
Ms Sturgeon said the number of children and young people being brought forward for tests had "increased significantly" in the two weeks since schools reopened.
"Last week alone, just short of 17,500 young people between two and 17 were tested," she said.
"That is a very significant number, but the key point I want to make from that is that of those, only 49 tested positive. That is a positivity rate of 0.3%."
The first minister said she could "well understand why many parents and teachers have a concern about the return to school".
But she said the figures revealed "the bigger picture", adding: "Despite an increase of more than 300% in testing of young people from one week to the next, the number of positive cases recorded increased by just two.
"That is encouraging, and I hope it's reassuring to parents and teachers across the country. I hope it will encourage people to absolutely continue to be vigilant, but not to be unduly concerned about young people in schools."
Ms Sturgeon urged parents to "remember the symptoms that trigger the need for a test", saying that a runny nose alone was not a reason to be tested.
The testing system has been hit by "exceptional demand" in recent days, with people in Glasgow and the central belt being directed to test centres in Inverness and Cumbria.
Ms Sturgeon said there "may have been some technical issues" which led to people being "directed erroneously to testing centres in England", and that work was ongoing to resolve the problem.
There have been concerns about clusters of the virus linked to schools, such as Kingspark School in Dundee which has had to be closed.
A total of 34 cases have now been linked to the school, including 21 staff and three pupils, but Ms Sturgeon said there was "no evidence of wider community transmission" of the virus.
The Scottish government has changed its guidance to recommend that pupils in secondary schools wear face coverings in corridors and communal areas from Monday of next week.
However ministers believe the spread of the virus is a bigger issue outside of schools, with the police to be given new powers from Friday to break up house parties.
Ms Sturgeon said "these kind of gatherings pose a significant transmission risk".
'My son's cough led to tests for all the family'
By Doug Kennedy
Just as things were heading towards some kind of "new normal", we've found ourselves stuck in lockdown again. My two boys haven't looked back since returning to the routine of uniform, drop-off, classes, after school, homework - not home schooling - and so on.
But they've also returned to the routine of new term sickness and bugs. First my youngest had a runny nose and a cold, which I picked up, and this then spread to my oldest. But my oldest's symptoms lingered to become a mild fever and a new, continuous cough. On that the advice is clear - new, continuous cough equals self-isolate and test.
Figures today confirm that this has been another part of the new normal for parents across Scotland, with more than 17,000 children tested in the past week. We, too, experienced the way this is squeezing the system, going through an hour of being offered the Isle of Bute as our closest available test - a two-hour trip with a ferry crossing.
Persistence got us to Prestwick Airport drive-through testing, so yesterday we headed down, went through the rigmarole of self-testing each other in the car and we are back at home, isolating, waiting for results.
These should come on Friday and hopefully confirm nothing more than the familiar cycle of school age coughs and colds. In the meantime we're back under each other's feet and making the most of this new, new normal.
A total of 20,056 people in Scotland have now tested positive for Covid-19, with 257 currently being treated in hospital.
But there have been no further deaths linked to confirmed cases of the virus since Ms Sturgeon announced that two people had died on Wednesday.
Ms Sturgeon warned that the virus "is still out there and is not going away", adding: "People are still dying of this virus, so we must continue to treat the threat of Covid seriously."
The first minister also said the Scottish government was monitoring a pilot scheme in England that will pay people on low incomes £13 a day if they have to self-isolate and cannot work from home.
The payment, announced by UK Health Secretary Matt Hancock on Thursday, applies to benefit claimants who live in areas where there are high numbers of coronavirus cases.
The England-wide scheme will begin with a trial in areas of north west England where there have been tighter lockdown measures after a rise in cases.
Ms Sturgeon said: "We have been encouraging the UK government to put in place support, and we are ascertaining the details.
"It seems to me to make sense for that to be administered through existing welfare or benefits systems, and obviously we are seeking to understand what the financial consequential position is for the Scottish government."
She said the Scottish government would then take a decision of its own once it had the information it needed.