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An Australian woman attacked by a bull shark in Sydney Harbour has thanked her "heroic" neighbours for coming to her aid.

Lauren O'Neill was bitten during a sunset swim near a wharf on Monday.

The 29-year-old's leg was severely injured but surgeons worked through the night to save it from amputation, according to Sydney's Daily Telegraph.

In a statement on Wednesday, Ms O'Neill lauded the life-saving help offered by onlookers, medical staff and police.

She said she had been taking a "short dip" close to the shore in Elizabeth Bay after a hot day - as she often did - when she was attacked.

"She wishes to thank her heroic and very kind neighbours for the critical assistance they provided her," said a statement released by the hospital where she is receiving care.

Local media have reported that the keen kayaker and swimmer lived near an ocean pool equipped with shark nets but often swam in the open water.

Witnesses have said they rushed to the scene and applied first aid after hearing her yelling. They helped Ms O'Neill out of the water and one woman - a vet - applied a tourniquet to stem the bleeding, something credited with potentially saving her life.

Ms O'Neill said she was "immensely grateful" to paramedics and police for their "swift and caring actions at the scene" as well as the medical teams treating her.

"Her likely full recovery is testament to their extraordinary skills," the statement said.

She also thanked her loved ones and the public for their support, but requested privacy as she recovers.

Sydney Harbour is a well-known habitat for bull sharks, but attacks in the area are rare.

Experts have reiterated warnings to locals to stay out of the harbour on hot days and at dawn or dusk - times of greater shark activity.