CYCLISTS should stick to the roads, says North Sydney Mayor Jilly Gibson.

Further, all NSW cyclists should be licensed and registered so that those who speed or cycle aggressively can be penalised for flouting road rules.

"Commuter cyclists are capable of speeding faster than cars during peak times. Some travel at 30-40km/h if a pedestrian is hit by a bike at that speed, they could be killed," Cr Gibson said.

Her comments come after the council recently shelved plans to upgrade the St Leonards Park shared path, following an incident where an angry cyclist got off his bike and shoved a pedestrian walking his dog.

"A white line does nothing to stop toddlers or the elderly from accidentally straying into the path of a cyclists footpaths are made for feet, cyclists should stick to roads," Cr Gibson said.

A petition, signed by 80 residents, calling for St Leonards Park to be for pedestrian and leisure cycling activity only (no commuter cycling), was lodged with the council this month.

Neutral Bay resident Pamela Notley said cyclists should ride on a separate path around the edge of St Leonards Park.

"Some cyclists are extremely abusive. Pedestrians have a right to walk safely," she told Tuesday night's council meeting.

However, Bike North president Darryn Capes-Davis said it was unfair to force cyclists onto roads without designated bike lanes.

He also questioned a 10km/h speed limit, saying joggers could run faster and cyclists were less stable at slow speeds.