The two men were part of a group of nine pirates who were in a boast approaching an unidentified ship near the Gulf of Aden when a naval force opened fire on them, said Ahmed Abdullahi, an official with the anti-piracy force in Puntland, a semi-autonomous part of Somalia.
The six other pirates survived the attack and escaped, he said.
Residents in Durduri, a coastal village in Sanaag region, said they found two dead bodies left by the pirates near the coast on Sunday morning.
In recent weeks there has been a resurgence of piracy off Somalia's coast, after five years of inactivity.
In a separate incident in Somalia, a roadside bomb on Sunday struck a convoy carrying officials from the World Food Program on the outskirts of Mogadishu, injuring two bodyguards, a U.N. official said.
The U.N. officials were on a supervision mission outside Mogadishu at the time of the attack, the official said on condition of anonymity because he was not authorized to speak to the press.
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