Thirty four people died after a boat packed with scuba divers caught fire near an island off the Southern California coast and authorities have called off the search for survivors.

The US Coast Guard and police said no one has been found alive after flames tore through the dive boat early on Monday as passengers on a recreational scuba diving trip slept below deck.

The Conception carried 33 passengers and six crew members, and only five of the crew sleeping on the top deck were able to escape by jumping off. They were rescued by a pleasure boat moored nearby.

Investigators have not yet determined how the fire broke out.

Santa Barbara county sheriff Bill Brown said the bodies of 20 victims have been recovered and divers have seen between four and six others in the sunken wreckage.

Santa Barbara County Sheriff Bill Brown says most of the bodies need to be identified by DNA analysis. Photo: Getty

He said authorities are trying to stabilise the boat that sank in about 18 metres of water so divers can recover those remains.

Most need to be identified by DNA analysis and officials are collecting samples from family members, Brown said.

One passenger, marine biologist and veteran diver Kristy Finstad, 41, was identified in a Facebook post by her brother, Brett Harmeling of Houston.

“Please pray for my sister Kristy!! She was leading a dive trip on this boat,” Harmeling wrote.

The 39 had departed Santa Barbara Harbour on Saturday aboard the boat for a Labour Day weekend trip.

The fire broke out about 3am on Monday as the Conception was anchored off Santa Cruz Island, about 145km west of Los Angeles.

The crew appeared to quickly call for help.

“The call was garbled, it was not that clear, but we were able to get some information out of it to send vessels,” Coast Guard Petty Officer Mark Barney said.

Captain Paul Amaral of the vessel assistance company TowBoatUS also launched a fast boat from Ventura Harbour, but it was about 48km away.

By the time it got there around 5am, a Coast Guard helicopter and a fireboat were on the scene.

Amaral said he first searched the water and shoreline, then turned back to the Conception, which was adrift.

He attached a line and pulled it into deeper water so the fireboats could reach it.

“We launched that boat knowing that the vessel was on fire, lots of people aboard,” he said.

The five crew members, meanwhile, went on a dinghy to a private fishing boat, The Grape Escape, that was anchored near the north shore of Santa Cruz Island.

That boat’s owners, Bob and Shirley Hansen, told The New York Times they were asleep when they heard pounding on the side of their vessel about 3.30am and discovered the frightened crew members.

“When we looked out, the other boat was totally engulfed in flames, from stem to stern,” Hansen said.

“I could see the fire coming through holes on the side of the boat. There were these explosions every few beats. You can’t prepare yourself for that. It was horrendous.”

Hansen said two of the crew members went back towards the Conception looking for survivors but found no one.

The 23m Conception was on a three-day excursion to the chain of rugged, wind-swept isles that form Channel Islands National Park in the Pacific Ocean west of Los Angeles.

The fire broke out as the boat sat anchored in Platt’s Harbour off Santa Cruz Island.

-AAP