Hostage captain rescued, 3 pirates killed

* Official: U.S. forces kill 3 pirates after seeing captain in "imminent danger"

* American captain freed after being held hostage by pirates since Wednesday

* Richard Phillips is uninjured, in good condition, U.S. official says

* Maersk Alabama and its American crew was attacked by pirates off Somali coast

U.S. forces killed three pirates Sunday and rescued cargo ship Capt. Richard Phillips, held hostage in a lifeboat since Wednesday, after seeing him in "imminent danger," a senior defense official told CNN.

The official contradicted earlier reports that the captain jumped into the water off Somalia on Sunday.

Three of the pirates on the lifeboat with Phillips were shot and killed, the official said. A fourth pirate was aboard the nearby USS Bainbridge negotiating Phillips' fate when the shootings occurred, he said.

Phillips was uninjured and in good condition after his rescue at 7:19 p.m. (12:19 p.m. ET), according to a senior U.S. official.

Phillips has contacted his family and received a routine medical exam, the U.S. Navy Central Command said in a statement.

Alison McCall, a spokeswoman for Maersk, owner of the Alabama, read a statement from Phillips' family to reporters:

"The Phillips family wants to thank you all for your support and prayers. They have felt the caring and concern extended by the nation," McCall said. "This is truly a very happy Easter for the Phillips family."

Phillips offered himself as a hostage after the pirates stormed the U.S.-flagged ship Wednesday morning, according to Maersk. The pirates retreated to the lifeboat with Phillips, leaving the Alabama with its crew.

Phillips tried to escape by diving off the 28-foot, covered lifeboat Thursday night, but one of the pirates dove into the Indian Ocean to retrieve him.

Maersk Line Limited, owner of the Maersk Alabama, issued a statement saying it was informed at 1:30 p.m. Sunday by the U.S. government that he had been rescued. John Reinhart, president and CEO, called Phillips' wife, Andrea, to tell her the good news.

Maersk Alabama crew members, who guided the ship to Kenya over the weekend, were "jubilant" when they received word of the rescue, the statement says.

Reinhart told reporters Sunday afternoon that the company and Phillips' family was ecstatic that he was rescued.

"He's a leader of men. He's a brave and courageous man. He persevered through difficult times," Reinhart said.

He said he talked with Phillips after his rescue, and that he asked Phillips whether he had a message for the news media.

"He said ... 'The heroes are the Navy, the SEALs, and those who brought me home,' " Reinhart said.

A man who answered the door at Phillips' home in Underhill, Vermont, on Sunday afternoon told CNN's Stephanie Elam that the family had known the news for hours. He said details would have to come from Virginia, apparently referring to Maersk's home base in Norfolk.

At the White House, President Obama issued a statement saying he is "very pleased that Capt. Phillips has been rescued and is safely on board the USS Boxer."

"His safety has been our principal concern, and I know this is a welcome relief to his family and his crew," Obama's statement said. "We remain resolved to halt the rise of piracy in this region. To achieve that goal, we must continue to work with our partners to prevent future attacks, be prepared to interdict acts of piracy and ensure that those who commit acts of piracy are held accountable for their crimes.

On Saturday, the FBI launched a criminal investigation into Wednesday's hijacking of the U.S.-flagged cargo ship by Somali pirates, two law enforcement officials told CNN. The probe will be led by the FBI's New York field office, which is responsible for looking into cases involving U.S. citizens in the African region, the officials said.

Snippets of information started to emerge Saturday about how the Maersk Alabama's crew managed to retake the ship after it was hijacked by pirates Wednesday about 350 miles off the coast of Somalia in the Indian Ocean.

The Alabama reached port in Mombasa, Kenya, on Saturday. Crew members aboard the freed cargo ship described how some of their colleagues attempted to "jump" their pirate captors.

A scuffle ensued and one of the sailors stabbed a pirate in the hand in the battle to retake the container ship, one of the sailors told CNN.

Crew members smiled broadly as they stood on the ship's deck under the watchful eyes of security teams. Although the crew was kept away from the media, CNN's Stan Grant got close enough to ask crew members what happened after the pirates climbed aboard the ship.

One crew member said he recalled being awakened around 7 a.m. as the hijacking began.

"I was scared," Grant quoted the man as saying.

Some of the crew managed to hide in a secure part of the Alabama as the pirates stormed the ship, the sailor said.

As the sailors described their clash with the pirates, a crew member pointed to one shipmate and said, "This guy is a hero. He and the chief engineer, they took down the pirate. ... He led him down there to the engine room, and then they jumped him."

The shipmate added that he stabbed the pirate's hand and tied him up.

"Capt. Phillips is a hero," another crew member shouted from the deck of the freed ship.

Maersk CEO Reinhart told reporters Saturday that the crew will stay on board in Mombasa while the FBI conducts an investigation.