Australian police and wildlife officers were ordered yesterday to destroy a large shark which killed a teenage surfer in a savage attack as his horrified schoolfriends looked on.

Police said searchers had found a small amount of what were believed to be human remains which they had sent for forensic testing. A search in glassy waters off popular West Beach in the South Australia state capital Adelaide was continuing, they said.

"We're still searching... they may have found a couple more things that could be human remains," a police spokeswoman said.

Witnesses described on Thursday seeing two great white sharks - one up to five metres long - attack 18-year-old attack surfer Nick Peterson after he fell off a surfboard which friends were towing behind a small boat about 300 metres offshore. However, police and rescuers now believe one large shark killed the teenager, the second fatal shark attack in Australia in five days.

Acting South Australia state premier Kevin Foley said the shark should be killed if it was found even though great white sharks are a protected species in Australian waters.

"The government's view is that a large shark in close proximity to the beaches that is posing a direct threat to human life should be destroyed," Mr Foley told reporters in Adelaide.

Beaches in the area remained open and swimmers ventured back into the water despite Thursday's savage attack.

Rescue workers reported seeing a four-metre shark yesterdal several kilometres north of West Beach and believe it was the same one seen in the area several times in recent weeks.

"It actually came to the surface and swam under our rescue boat, so we do know it's still in the area," Sea Rescue Squadron leader Fraser Bell told reporters.

"The shark was seen... and headed south towards the scene of yesterday's attack," he said.

While the search continued, distraught members of Peterson's family and his friends gathered at the beach and linked arms in a group at the water's edge. Others laid flowers along the shore.

"Nick was a very passionate and a very experienced water man," Mr Peterson's father Philip said.

"We acknowledge that the sea is in fact the shark's domain and we don't... advocate the indiscriminate killing of any shark," he said in a statement read to reporters.

Police inspector David Lusty said the attack had been swift and savage and that Mr Peterson's friends could have done nothing to help him.

A 38-year-old man died after he was mauled by a shark while spearfishing off the far northeast coast of tropical Queensland state last Saturday.

In July, another surfer died in Western Australia when he was attacked by a shark described as being "as big as a car".

Australia has a reputation for shark attacks but International Shark File figures show most occur in North American waters.

The first documented attack in Australia was in 1791 and there have been more than 625 attacks in the past 200 years, about 190 of them fatal.