United States navy snipers opened fire and killed three pirates holding an American captain at gunpoint, delivering the skipper unharmed and ending a five-day high-seas hostage drama on Easter Sunday.

The pirates were pointing AK-47s at Captain Richard Phillips and he was in "imminent danger" of being killed when the commander of the nearby USS Bainbridge made the split-second decision to order his men to shoot, Vice-admiral Bill Gortney said.

Phillips' crew, who said they had escaped the pirates after Phillips offered himself as a hostage, erupted in cheers aboard their ship docked in Mombasa, Kenya. Some waved American flags and fired flares in celebration.

The navy's 5th Fleet said Phillips, 53, was resting comfortably after a medical exam on the San Diego-based USS Boxer in the Indian Ocean, off the coast of Somalia. Gortney said the captain had been "tied up inside the lifeboat" over much of the ordeal.

"I'm just the byline. The real heroes are the Navy, the Seals, those who have brought me home," Phillips said by phone to Maersk Line Limited President and CEO John Reinhart, the company head told reporters.

Fourth pirate

US officials said a fourth pirate had surrendered and was in military custody.

The rescue was a dramatic blow to the pirates who have preyed on international shipping and hold more than a dozen ships with about 230 sailors from a variety of nations. But it also risked provoking retaliatory attacks.

Jamac Habeb, a 30-year-old self-proclaimed pirate, told The Associated Press from Eyl, one of Somalia's piracy hubs: "From now on, if we capture foreign ships and their respective countries try to attack us, we will kill them (the hostages)."

The Department of Defence twice asked President Barack Obama for permission to use military force to rescue Phillips, most recently late Friday evening, US officials said. On Saturday morning, Obama signed off on the Pentagon's request, as he had a day earlier.