Local councillors and parents are demanding answers after two serious incidents, one of which left seven children injured.
It comes after the Evening Times revealed Holyrood Secondary School has gone into lunchtime "lockdown" amid fears about pupils' safety.
Education bosses have banned children from leaving the school - Glasgow's largest - at the break.
The strict lunchtime policy comes just days after parents demanded to know how intruders could get into the school.
Police have now been drafted in to stand guard at the school gates.
South Central Councillor Soryia Siddique, said: "I have raised the recent incidents of disorder involving pupils from Holyrood Secondary with the director of education.
"There is an increased police presence around the school. Safeguarding our youth is a priority.
"I will be liaising with the department of education and the police to ensure the promotion of positive behaviour is of priority."
As we reported, seven teenagers were hurt after incidents near Holyrood Secondary on Monday afternoon.
Police confirmed three pupils have been reported to the procur-ator fiscal and children's reporter in connection with the incidents.
One mother said: "Keeping our children in school all day isn't practical and it can't continue forever.
"We need to get to the bottom of what is happening at Holyrood and simply banning the children from leaving school isn't the solution.
"The security of the whole school, and surrounding areas, need to be looked at."
Her comments were echoed by local SNP councillor Mhairi Hunter.
She said: "I will be asking questions of both the education depart-ment and the school. This is obviously extremely worrying.
"Parents expect their children to be safe in school."
An investigation was launched into the incident at the school last Wednesday, when three youths entered the school, which has more than 2000 pupils and 130 teachers.
Meanwhile, other concerned parents said they would be walking their children to and from school after the incident.
Glasgow City Council said officials were looking into a "number of short-term options" to keep pupils at the Govanhill school safe.
A spokeswoman said: "We have been comm-unicating with parents and local councillors about the recent incidents involving the school. The safety of our young people is paramount."
Education bosses said a letter was sent out to all parents to reassure them.