Police presence at a number of schools had been increased in response to the trend and high visibility patrols would be carried out throughout Friday, the spokesperson said.
Officers were working with partners in affected schools, monitoring relevant social media activity and “carrying out frequent intelligence checks”.
They said any reported incidents would be investigated, and anyone involved in violence would be “dealt with swiftly and robustly”.
Deirde Clearly, head teacher at Notre Dame High School, wrote to parents and said the “so-called red vs blue school wars” were causing “concern and anxiety” across the city.
“There’s an ongoing multi-agency response in place and this involves the police, safeguarding hub and local authority,” she said, adding that officers had visited affected schools on Thursday.
“While we do not want to cause unnecessary concern, it is important that students are aware and cautious,” she added.
“Students were also reminded of our values as a school and the importance of us all working together to ensure everyone feels safe.”
She asked pupils to avoid commenting or sharing social media posts and to head straight home after school.
Clearly also asked parents and guardians to monitor their child’s social media.