Image caption Scott and Jean Adam first set sail on the 58-foot craft in 2002

Four Americans hijacked by Somali pirates off the coast of Oman have been killed by their captors, US defence officials say.

The US military said its forces trailing the vessel had responded to gunfire heard aboard but found all the captives shot when they arrived.

The yacht S/V Quest, hijacked on Friday, was owned and sailed by Scott and Jean Adam of California.

Also killed were two US passengers, Phyllis Macay and Bob Riggle.

'Shot by captors'

US Central Command said that negotiations were under way between the US Navy and the pirates, when the US forces heard gunfire coming from the Quest about 0600GMT.

US Navy Seal special forces sailors boarded the ship without firing a shot, then killed two pirates while they were taking control of the ship.

They discovered the four Americans shot. At least one - Ms Macay - was alive when the Seals boarded. The US Navy Seals attempted unsuccessfully to save the injured hostages, the military said.

"As they responded to the gunfire, reaching and boarding the Quest, the forces discovered all four hostages had been shot by their captors," Gen James Mattis of US Central Command Commander said in a statement.

As they responded to the gunfire, reaching and boarding the Quest, the forces discovered all four hostages had been shot by their captors Gen James Mattis, US Central Command Pirate violence grows

"We express our deepest condolences for the innocent lives callously lost aboard the Quest," the statement added.

But the BBC's Will Ross in Nairobi says the pirates' telling of the encounter differs from the US Navy's. The pirates report the US warship attacked first, killing two pirates, and the hostages were killed in retaliation.

The incident will provoke further debate on whether the use of force is wise when dealing with Somali pirates who have already taken hostages, our correspondent says.

Obama notified

Media playback is unsupported on your device Media caption Friends paid tribute to Jean and Scott Adam who were cruising around the world distributing Bibles

According to the US military, four Navy warships - including an aircraft carrier - began tracking the hijacked vessel on Friday and were following it toward the Somali coast, hoping to prevent the pirates from disembarking with the hostages.

The White House said President Barack Obama on Saturday had authorised the use of force in the case of "an imminent threat" to the hostages. He was notified of the hostages' deaths soon after they were killed, spokesman Jay Carney said.

On Tuesday, Navy officials told reporters that two pirates had boarded a naval vessel for negotiations when the pirate crew aboard the Quest fired a rocket-propelled grenade at their ship.

The grenade missed, and the US Navy sailors then heard gunfire aboard the Quest and dispatched the Navy Seal boarding party, which discovered the four Americans.

The US Navy captured 13 pirates, killed two - one with shots and another with a knife - and found the remains of two other pirates already dead about the vessel, the US military said.

It was unclear how they died.

'Responsible planners'

According to the Adams' website, the middle-aged couple set sail in 2002 on the 58-foot vessel, and in 2004 they embarked on a planned eight- to 10-year voyage around the world.

Before their capture, the sailors had crossed the Indian Ocean from Cochin, India, after calling at Phuket, Thailand and Sri Lanka. They hoped to disembark in Djibouti, then cross the Suez Canal before sailing to Crete in April.

Friends have described the Adams as adventure-seekers who were also driven by their Christian faith, at times distributing Bibles at ports of call.

Robert Johnston, who taught Scott Adam at Fuller Seminary in California, described the Adams as accomplished sailors.

"They were responsible planners, they knew there was the potential for problems and they tried to take precautions, but obviously something happened," he said before the group was reported killed.

Ms Macay's niece, Nina Crossland, told reporters her late aunt had planned ahead for the voyage.

"She was not haphazardly travelling around the ocean, loosely travelling around," Ms Crossland said.

"My aunt was very adventurous. If this was something that was going to scare her she would not be doing it."

The couple had also stopped updating friends on their location, in an apparent effort to keep their whereabouts secret from pirates.

Pirates currently hold about 30 boats captured off the coast of Somalia, with a total of more than 600 hostages, according to the US Navy.

Pirate attacks

Somalia has had no functioning central government since 1991, allowing piracy to flourish off its coast.

Somali pirates have made millions of dollars in recent years by capturing cargo vessels in the shipping lanes around the Horn of Africa and holding the ships and crew for ransom.

A recent US study found that maritime piracy costs the global economy between $7bn (£4.4bn) and $12bn (£7.6bn) a year.

The US has gained recent experience prosecuting pirates in civilian courts.

Last week, a Somali man who pleaded guilty to a pirate attack on a US-flagged merchant ship was sentenced to more than 33 years in prison.

Abdiwali Abdiqadir Muse is the only survivor of the crew of pirates who attacked the Maersk Alabama merchant ship off Somalia's coast in April 2009.

He was captured by the US Navy, whose sharpshooters killed three other pirates trying to escape on a lifeboat with the Alabama's American captain.