But the BBC's Will Ross in Nairobi says the pirates' telling of the encounter differs from the US Navy's. The pirates report the US warship attacked first, killing two pirates, and the hostages were killed in retaliation.
The incident will provoke further debate on whether the use of force is wise when dealing with Somali pirates who have already taken hostages, our correspondent says.
According to the US military, Navy warships began tracking the hijacked vessel on Friday and were following it toward the Somali coast.
Navy officials told reporters on Tuesday that two pirates had boarded a naval vessel for negotiations when the pirate crew aboard the Quest fired a rocket-propelled grenade at their ship.
The US Navy sailors then heard gunfire aboard the Quest and dispatched a boarding party, which discovered the four Americans' bodies.
The US Navy captured 13 pirates, killed two - one with shots and another with a knife - and found the remains of two other pirates already dead about the vessel, the US military said.
BBC News
