Gortney says the pirates threatened throughout the ordeal to kill Phillips. Gortney says the pirates were armed with AK-47s and small-caliber pistols, and were pointing the AK-47s at the captain.
Gortney says the commander of the nearby USS Bainbridge believed Phillips was in "imminent danger" when he ordered sailors to fire at the armed pirates.
Gortney says the White House had given "very clear guidance and authority" that if any time the commander Capt. Phillips' life was in danger to take action to make sure it was not.
Gortney spoke in a telephone conference call from Bahrain. He is the commander of U.S. Naval Forces Central Command.
A senior U.S. intelligence official said hostage Richard Phillips was not hurt in what appeared to be a swift firefight off the Somali coast on Sunday. Phillips was safely transported to a Navy warship nearby.
The official said three pirates were killed.
The official said a pirate who had been involved in negotiations to free the American but who was not on the lifeboat where the captain was being held was taken into custody.
The official was not authorized to discuss the matter publicly and spoke on condition of anonymity.
A Pentagon spokesman did not have an immediate comment.
The company that owns the American ship seized this week by Somali pirates says the captain that has been held hostage for days has been rescued.
Maersk Line Limited President and CEO John Reinhart said in a news relaese that the U.S. government informed the company around 1:30 p.m. Sunday that Richard Phillips had been rescued. He was to hold a media briefing later Sunday.
Reinhart said the company called Phillips' wife, Andrea, to tell her the news. He said the crew of the Maersk Alabama was "jubilant" when they received word that Phillips was safe.
Phillips was being held captive on a lifeboat after his ship was boarded by pirates days ago. The rest of the crew and the ship have made it safely to a port in Kenya.