A senior Dundee councillor said parents must take action if they suspect their children have been involved in fire-raising.
Police in Dundee believe a blaze in the former St Vincent’s RC Primary School on Pitkerro Road was started deliberately on Wednesday night.
Teenagers have also been charged in connection with two other recent blazes in the city that are alleged to have been started on purpose, at Braeview Academy and the former Hilltown Indoor Market.
Lochee councillor Alan Ross, the convener of the public protection and community safety committee, said it was lucky no one had been injured or killed in any of the fires across Dundee over recent weeks.
Mr Ross said: “The fire at the former St Vincent’s was disappointing but it is also quite worrying.
“These people are putting the emergency services under severe pressure and they are obviously putting themselves, and potentially others, into extremely dangerous situations.
“Thankfully nobody has been injured but there had been people in Braeview just before the fire, albeit in a different part of the building.
“If somebody set a fire and then somebody was seriously injured, how could they live with themselves?”
The SNP councillor added parents are likely to know if their children have been setting fires, or putting their lives at risk by playing near them.
He said: “I would imagine parents must have noticed the smell if their children have started a fire.
“It’s an incredibly dangerous thing to do, not just for them but for everybody.”
Mr Ross added: “It also creates a lot of financial pressure on the council at a time when things are stretched.”
Fire crews were called to St Vincent’s RC Primary School around 6.15pm on Wednesday.
The former primary school had been broken into a short time before the fire started.
A number of youths were seen entering the school, which closed in the summer, at around 5.20pm.
Police said all were in their mid-teens.
The fire was quickly extinguished by Scottish Fire and Rescue Service.
Police Scotland is asking for anyone that may have information to contact them with the reference CR/25327/18.
A 15-year-old boy has been charged by police in connection with the fire at Braeview Academy on September 11.
The school has been closed since the blaze with pupils sent to classes at Cragie High School and Baldragon Academy.
Twenty-four hours after the fire at the Whitfield school, the Hilltown Indoor Market and an adjacent gym were destroyed in another fire.
Four teenagers were subsequently charged by police in connection with that incident.