The marine predator struck on Sunday afternoon while the boy and his friends were jumping into the water off the harbour’s Shark Beach.

“It was a horrendous scene at the time when police attended. We believe it was something like a bull shark that attacked the lower limbs of that boy,” said superintendent Joseph McNulty, New South Wales marine area police commander.

“That boy is fighting for his life now.”

At the time of the attack, the children were leaping into the water off a 6m rock in the eastern Sydney suburb of Vaucluse.

Recent heavy rain had drained into the harbour, turning the water murky, police said.

“We believe the combination of the brackish water, the fresh water, the actions of the splashing may have made that perfect storm environment for that shark attack yesterday,” McNulty told reporters.

He praised the boy’s “gallant” young friends for going to his aid before police arrived.

“He had been bitten by a large shark,” McNulty said.

Officers pulled the unconscious child on to a police boat and gave him first aid, applying two tourniquets to stem the bleeding from the boy’s legs, he said.

They tried to resuscitate the boy as they sped across the harbour to a wharf where ambulance paramedics were waiting.

The child, confirmed by police to be 12 years old, is in intensive care at Sydney Children’s Hospital surrounded by family and friends, McNulty said.

There have been more than 1,280 shark incidents around Australia since 1791, of which more than 250 resulted in death, according to a database of the predators’ encounters with humans.

Increasingly crowded waters and rising ocean temperatures that appear to be swaying sharks’ migratory patterns may be contributing to a rise in attacks despite overfishing depleting some species, scientists say.

A great white shark mauled surfer Mercury Psillakis to death at a popular northern Sydney ocean beach in September.

Two months later, a bull shark killed a woman swimming off a remote beach north of Sydney.