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NAIROBI, Kenya — Four Americans taken hostage by Somali pirates off East Africa were shot and killed by their captors Tuesday, the US military said, marking the first time US citizens have been killed in a wave of pirate attacks plaguing the Gulf of Aden and the Indian Ocean for years.US naval forces who were trailing the Americans' captured yacht with four warships quickly boarded the vessel after hearing the gunfire. They tried to provide lifesaving care to the Americans, but they died of their wounds, US Central Command in Tampa, Florida said in a statement.A member of a US special operations force killed one of the pirates with a knife as he went inside of the yacht, said Vice Adm. Mark Fox, commander of US naval forces for Central Command.Fox said in a televised briefing that the violence on Tuesday started when a rocket-propelled grenade was fired from the yacht at the USS Sterett, a guided-missile destroyer 600 yards (meters) away. The RPG missed and almost immediately afterward small arms fire was heard coming from the yacht, Fox said.President Barack Obama, who was notified about the deaths at 4:42 a.m. Washington time, had authorized the military on Saturday to use force in case of an imminent threat to the hostages, said White House spokesman Jay Carney.A total of two pirates, including the one who was knifed, died during the ensuing confrontation — which happened around 9 a.m. East Africa time — and 13 were captured and detained, the Central Command said. The remains of two other pirates who were already dead for some time were also found. The US military didn't state how those two died. It was unclear if the pirates had fought among themselves.Negotiations had been under way to try to win the release of the two couples on the pirated vessel Quest when the gunfire was heard, the US military said. Fox, asked by reporters about the nature of the negotiations, said he had no details.He identified the slain Americans as Jean and Scott Adam, of Marina del Rey near Los Angeles, and Phyllis Macay and Bob Riggle, of Seattle, Washington.The Quest was the home of the Adams who had been sailing around the world since December 2004 with a yacht full of Bibles.Pirates hijacked the Quest on Friday several hundred miles south of Oman. Fox said mariners are warned about traveling through the area because of the dangers of pirate attacks.Gen. James N. Mattis, commander of US Central Command, said: "We express our deepest condolences for the innocent lives callously lost aboard the Quest."In total the US said that 19 pirates were involved in the hijacking of the Quest.Two days before the attack, a New York court had sentenced a pirate to 33 years in prison for the 2009 hijacking of the Maersk Alabama, a US cargo vessel. That hijacking ended when Navy sharpshooters killed two pirates holding the ship's captain. A pirate in Somalia told the AP last week that pirates were more likely to attack Americans because of the verdict."It's a black day for us and also the Americans, but they lost bigger than us," a pirate who said his name was Bile Hussein said Tuesday. "If they still want a solution and safety for their citizens in the oceans, let them release our men they arrested."At the Seattle Singles Yacht Club, where Riggle and Macay were members, Joe Grande said the two were "great sailors, good people. They were doing what they wanted to do, but that's small comfort in the face of this."Only minutes before the military announced that the four Americans had died, a Somali pirate told The Associated Press by phone that if the yacht were attacked, "the hostages will be the first to go.""Some pirates have even suggested rigging the yacht with land mines and explosives so as the whole yacht explodes with the first gunshot," said the pirate, who gave his name as Abdullahi Mohamed, who claimed to be a friend of the pirates holding the four Americans.The military said US forces have been monitoring the Quest for about three days, since shortly after the Friday attack. Four Navy warships were involved, including the aircraft carrier USS Enterprise.The killing of the four Americans appears to underscore an increasingly brutal and aggressive shift pirates have been showing toward hostages. The conventional wisdom in the shipping industry had been that Somali pirates are businessmen looking for a ransom payday, not insurgents looking to terrorize people.