The US captain taken hostage by Somali pirates managed to jump off their lifeboat overnight but was recaptured, according to US media reports.

The escape attempt by Capt Richard Phillips was witnessed by a US navy ship nearby but happened too fast for it to come to his aid, NBC News says.

He was captured after a struggle on his ship, Maersk Alabama. Pirates seized the ship but the crew fought them off.

There are thought to be four pirates with Capt Phillips in the lifeboat, which has reportedly run out of fuel, and it is not yet clear what they are demanding.

The Maersk Alabama is reportedly sailing for the Kenyan port of Mombasa under armed guard.

Gen David Petraeus, head of US Central Command, said reinforcements would arrive within 48 hours, adding that a warship was already very close to the lifeboat.

But other hijacked ships with hostages aboard are also reported to be nearing the area to support the pirates on the lifeboat.

The cruise-missile carrying USS Bainbridge was sent to the scene in a move analysts say will strengthen the hand of US negotiators.

The destroyer is shadowing the lifeboat, and its officers are talking to the pirates, as well as giving them food and batteries for a two-way radio.

Capt Phillips has a radio and contacted the navy and crew of his ship to say he was unharmed, the Maersk shipping company said in a statement.

MANAMA, Bahrain (CNN) -- U.S. Navy snipers fatally shot three pirates holding an American cargo-ship captain hostage after seeing that one of the pirates "had an AK-47 leveled at the captain's back," a military official said Sunday.

The captain, who'd been held in a lifeboat in the Indian Ocean since Wednesday, was rescued uninjured, Navy Vice Adm. Bill Gortney told reporters.

Capt. Richard Phillips' ship, the Maersk Alabama, was stormed by pirates 350 miles off Somalia on Wednesday morning. He was "resting comfortably" on the USS Boxer after his rescue Sunday night, according to the Navy.

Phillips contacted his family and received a routine medical exam after his rescue at 7:19 p.m. (12:19 p.m. ET), the Navy Central Command said.

"The captain is in good health. He's showered up and in a clean set of clothes," Gortney said in a telephone news conference from Navy Central Command in Bahrain.

U.S. forces moved to rescue Phillips after seeing him in imminent danger on the lifeboat, Gortney said. A fourth pirate was negotiating Phillips' fate aboard the nearby USS Bainbridge.

"While working through the negotiations process tonight, the on-scene commander from the Bainbridge made the decision that the captain's life was in immediate danger, and the three pirates were killed," Gortney said. "The pirate who surrendered earlier today is being treated humanely; his counterparts who continued to fight paid with their lives."

The three pirates, who were armed with AK-47 rifles, were killed by shooters who were aboard the Bainbridge, Gortney said.