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.