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Graeme Gibbon-Brooks, the head of Dryad Maritime Intelligence, said he was confounded by the turn of events.

“We have heard threats against the lives of Americans before, but it strikes me as being very, very unusual why they would kill hostages outright,” he said, adding that the pirates must realize that killing Americans would invite a military response.

The military said U.S. forces had 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.

Last week, a Somali pirate was sentenced to 33 years in prison by a New York court for the 2009 hijacking of the Maersk Alabama, a U.S. cargo vessel. That hijacking ended when Navy sharpshooters killed two pirates holding the ship’s captain.

pirate in Somalia told the AP last week that pirates were more likely to attack Americans because of the verdict.

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 was that Somali pirates were businessmen looking for a ransom payday, not insurgents looking to terrorize people.

The pirates — who currently hold 30 ships and more than 660 hostages — typically win a multimillion-dollar ransom for releasing their captives, a huge sum that is shared among investors and pirates. The money often is spent on alcohol, drugs and prostitutes. One ransom paid last year was reported as $9.5 million. Most ransoms are worth several million dollars.

Given that typical financial motivation, Tuesday’s killings left several unanswered questions, such as whether the four hostages had tried to take over the yacht from the pirates or if the American forces spooked the pirates by approaching the yacht.

Pirates have increased attacks off the coast of East Africa in recent years despite an international flotilla of warships dedicated to protecting vessels and stopping the pirate assaults.

Mr. Mohamed, the pirate in Somalia, told the AP that pirate leaders had been expecting the yacht to make landfall soon.

Five cars full of pirates were headed toward the pirate dens of Eyl and Gara’ad in anticipation of the Quest’s reaching land Monday, he said. Had the four reached land, they may have faced a long hostage ordeal, such as the 388 days that the British sailing couple Paul and Rachel Chandler spent in the hands of pirates. The two were released in November.

Omar Jamal, first secretary at Somalia’s mission at the United Nations, sent his condolences to the families of the four Americans and called the deaths a tragic loss of life. Mr. Jamal said there is an urgent need to address the piracy problem.

The Adams ran a Bible ministry and have been distributing Bibles to schools and churches in remote villages in areas including the Fiji Islands, Alaska, New Zealand, Central America and French Polynesia.

Associated Press reporter Pauline Jelinek in Washington contributed to this report.