"During the attempt by Nigerian military marines to free the seven hostages on the FPSO Mystras, gunfire was exchanged during which a hostage was killed while six others, one of whom was wounded, were freed and are safe," the group said on its website.
Italy's foreign ministry confirmed the death of one hostage.
ENI earlier identified the kidnapped oil workers as one Italian, one Briton, a Filipino, two Finns, a Pole and a Romanian.
The dead oilman was a British national and an injured hostage is Italian, the ANSA news agency reported, citing the Italian foreign ministry.
In Lagos, Nigerian police, who had earlier confirmed the kidnapping, denied all knowledge of the rescue attempt or of casualties.
No group has so far claimed responsibility for the latest such attack to rock Africa's biggest oil producer in recent months.

Copyright AFP (Agence France-Presse), 2006