The captain was unhurt and a fourth pirate was captured.
His crew had managed to fight off the armed pirates from the Maersk Alabama, but the captain was taken away in a lifeboat.
Among recent developments:
Another US ship, the Liberty Sun, was attacked by armed pirates, but escaped them with slight damage to the vessel.
The crew of the Maersk Alabama flew home to the US from the Kenyan city of Mombasa, but their captain's own return was delayed as he was still on the USS Bainbridge, the warship which had diverted to assist Liberty Sun.
One pirate said the attack on the Liberty Sun was revenge for the recent deaths of pirates.
The French navy captured 11 pirates after intercepting a command vessel about 550 miles (900km) off the coast of Kenya.
The Greek maritime ministry announced that a Greek cargo ship and its 24 crew, held by pirates since mid-March, had been released.
Secretary of State Hillary Clinton on plans to tackle piracy in the Gulf of Aden
The US four-point plan includes sending an envoy to the Somali donors' conference in Brussels on 23 April to work on plans to improve the situation in Somalia.
Mrs Clinton said the US would work with the Contact Group on Piracy Off the Coast of Somalia (CGPCS) to expand the multinational response to piracy.
She called for states to take responsibility for prosecuting and imprisoning captured pirates.
"These pirates are criminals, they are armed gangs on the sea, and those plotting attacks must be stopped."
Mrs Clinton called for continued work on releasing captured vessels, as several ships and their crews remain in the hands of pirates.
She also said the international group had to consider ways to track and freeze pirate assets.
"It is time to eliminate the financial payoff of piracy," she told reporters.
"We will also reiterate to all concerned the US policy of making no concessions or ransom payments to hostage takers."
The state department will set up meetings with members of the Somali Transitional Federal Government and regional leaders.
"We must press authorities within Somalia to take action against pirates operating from bases within their territory," Mrs Clinton said.
Making clear the threat was not just an issue for governments to resolve, she said the shipping industry had a joint responsibility.
"I have directed the [State] Department to work with shippers and the insurance industry to address gaps in their self-defence measures."
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