The 10-year-old boy was involved in a game with other students on Tuesday when he was allegedly assaulted and fell backwards at Wattawa Heights Public School in Bankstown, police have been told.

He remains in a critical but stable condition in Westmead Children's Hospital.

"It's understood the boy has a pre-existing medical condition," a NSW Police spokesperson said in a statement on Wednesday.

Officers have spoken with Wattawa Heights Public School students but no further police action is expected.

The NSW education department said the school was working with police to determine how the boy was injured. The family of the injured student has been offered support.

"When accurate information about what occurred is available the school will share that with parents and carers," a department spokesman told AAP.

"It is not appropriate for the school to provide detailed comment about this matter before police finish their investigation."

The age of criminal responsibility in NSW is 10.

The Australian Institute of Criminology says the presumption a child is incapable of crime exists under common law for those aged 10 to 13.