The ship identified as the Enrica Lexie fired at the fishermen in waters off India’s southern Kerala state on Wednesday, a navy statement said.
The Indian coast guard and navy vessels escorted the Italian ship to the nearby port city of Kochi and were questioning the captain and crew.
The owner of the fishing vessel, who goes by the single name Freddy, said Thursday the firing was unprovoked. The boat was fishing when the ship opened fire, killing the two fishermen instantly, he said.
Nine other fishermen onboard the craft survived.
Piracy has emerged as a major threat to merchant ships traversing the sea lanes of the Indian Ocean and Arabian Sea. Pirates based in Somalia have been hijacking ships and holding the vessels and their crew for ransom.
Several countries, including India, allow ship owners to deploy armed security guards on ships. Ship owners say the move has proved effective and prevented hijackings