The 17-year-olds were allegedly aboard one bike reported as stolen, and another believed to have been, on Toxteth Road in Glebe early on Thursday.

Officers asked them to stop for a random breath test but say they briefly accelerated before jumping off the bikes and running.

Police say they then fled to the end of the cul-de-sac on Toxteth Road, and jumped the fence.

However, there was a 10-metre cliff face on the other side.

One teen fell the full distance to the park below, suffered head injuries and was taken to hospital for surgery. He remains in a critical condition and is yet to be charged.

The other fell two metres to a rock ledge and suffered minor injuries. He was treated by paramedics and taken to Newtown Police Station.

He was on Thursday afternoon charged with vehicle theft, driving without a licence, failing to stop for police and breaching bail, and was refused bail to appear in a NSW children's court on Friday.

An officer also suffered minor injuries while attempting to reach the ledge.

Acting Assistant Commissioner Stacey Maloney on Thursday said both teens were from western Sydney and not Glebe residents.

The motorbike reported stolen was from southwestern Leumeah.

Ms Maloney also defended the officers' conduct, saying they acted appropriately in pursuing the teens after they took off.

The incident will be subject to a review.

"The police were doing what they were supposed to be doing, patrolling the area," Ms Maloney told reporters.

"They made the inquiries, reviewed the motorbike, (it) was stolen and they did everything at that point in terms of directing them to stop correctly."

Australian Associated Press