One other person from the Chinese-owned Fiji-flagged fishing vessel Tiro Two made it to a lifeboat and two others were found on another vessel.
They have all been interviewed by the police.
The Fiji Times newspaper reports that the chances of survival for the men who leapt into the water without any lifesaving equipment last Monday have been greatly reduced.
But Fiji Navy commander Captain Humphrey Tawake said the authorities remain optimistic.
The Chinese-owned, Fiji-flagged tuna longliner FV TIRO II was found on Wednesday by a New Zealand Air Force Orion about 90 nautical miles west of Fiji, with two crew members still onboard.
The Fijian Rescue Coordination Center has released photos of the two men found on board the vessel being handed over to police.
After taking on water Thursday night, FV TRIO II sank on Friday morning.
Earlier Captain Tawake told the Fiji Times they were aware of allegations that a Fijian national had beheaded a second Fijian national following a "heated argument" but said he could not comment further while a police investigation was underway.