Police believe a diver missing off the coast south of Perth may have been killed by a shark, after human remains were discovered with possible shark bites.

Michael McGregor, 38, failed to resurface after diving with two friends several kilometres off Dawesville Cut, about 80 kilometres south of Perth, early on Saturday afternoon.

Water Police divers yesterday found human remains believed to be that of the missing man close to the dive site.

In a statement, police said a preliminary investigation "indicates the male may have received shark bites".

However, they stressed the cause of death remained unclear and his friends did not see any shark attack.

Fatal shark attacks in WA since 2000 Surfer Chris Boyd: Gracetown, Nov 23, 2013

Surfer Chris Boyd: Gracetown, Nov 23, 2013 Surfer Ben Linden: Wedge Island, July 14, 2012

Surfer Ben Linden: Wedge Island, July 14, 2012 Diver Peter Kurmann: Geographe Bay, March 31, 2012

Diver Peter Kurmann: Geographe Bay, March 31, 2012 Diver George Wainwright: Rottnest Island, Oct 22, 2011

Diver George Wainwright: Rottnest Island, Oct 22, 2011 Swimmer Bryn Martin: Cottesloe Beach, Oct 10, 2011

Swimmer Bryn Martin: Cottesloe Beach, Oct 10, 2011 Surfer Kyle Burden: Bunker Bay, Sept 4, 2011

Surfer Kyle Burden: Bunker Bay, Sept 4, 2011 Surfer Nick Edwards: Gracetown, Aug 17, 2010

Surfer Nick Edwards: Gracetown, Aug 17, 2010 Snorkeler Brian Guest: Port Kennedy, Dec 27, 2008

Snorkeler Brian Guest: Port Kennedy, Dec 27, 2008 Snorkeler Geoffrey Brazier: Abrolhos Islands, Mar 18, 2005

Snorkeler Geoffrey Brazier: Abrolhos Islands, Mar 18, 2005 Surfer Brad Smith: Gracetown, July 10, 2004

Surfer Brad Smith: Gracetown, July 10, 2004 Swimmer Ken Crew: North Cottesloe, Nov 6, 2000

If Mr McGregor was taken by a shark it would be the first fatal attack since the State Government introduced baited drum lines off the WA coast in January.

Water police and volunteer marine rescue boats, together with a police dive team and helicopters, have been scouring the area since Saturday.

Police said further investigations were continuing and a report would be prepared for the coroner.

The waters off Western Australia have seen an unprecedented number of fatal shark attacks recently - including six fatal incidents in just over two years.

The last fatal shark attack in WA occurred in November, when surfer Chris Boyd was taken near Gracetown in the state's south-west.

Professional abalone diver Greg Pickering survived an attack near Esperance in October.

Meanwhile, a woman has been taken by a shark off the New South Wales far south coast town of Tathra.

Chris Armstrong, in her 60s, was swimming with a group between the wharf and Tathra Beach about 8:20am (AEDT).

The swimmers were about 100 metres offshore when they saw Ms Armstrong taken by what they believe was a shark.

According to the Australian Shark Attack File, there have been 85 recorded "unprovoked" attacks, 18 of which were fatal, in WA in the past 100 years.

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