A diver was killed by a large shark off the west Australian coast on Sunday in the country's second fatal attack in less than a week, police said.

The 60-year-old woman was diving with a man at a popular dive spot in the northern Perth suburb of Mindarie when the shark attacked, Western Australia state Police Inspector Danny Mulligan said.

"The man said that he felt something go past him and he turned around," Mulligan told reporters. "He didn't see the shark at that stage, but he felt it better to surface."

When the man reached the surface, he noticed commotion in the water, Mulligan said. Another boat arrived and the fishermen on board pulled him out of the water. They then spotted the woman and saw that she had suffered severe injuries.

The man was able to get back into his own boat and pull the woman from the water, but her wounds proved fatal, Mulligan said.

The fishermen said the shark was larger than their 5.3-meter (17-foot) boat, Mulligan said.

Beaches in the area were closed and the state fisheries department was trying to find and trap the shark.

The woman was the second person killed by a shark in Western Australia in less than a week. On Tuesday, a surfer's leg was bitten off by a shark about 100 kilometers (60 miles) south of where Sunday's attack occurred. Ben Gerring, 29, died from his injuries on Friday.

An inspection of Gerring's damaged surfboard showed a white shark was responsible. The fisheries department trapped and killed a large shark on Wednesday, but don't know if it was the same shark that attacked Gerring.