Fiji police have identified and hope to question a soldier this week over the death in military custody of a man, Nimilote Verebasaga, three months ago.
Mr Verebasaga died hours after being taken by armed troops from his home in Nakelo.
The acting police commissioner, Romanu Tikotikoca, has told the Fiji Times that police had a suspect who was a soldier, saying it was just a matter of time before police interviewed him.
He refused to elaborate.
Police are also investigating a group of soldiers in Nadi who are alleged to have caused fatal injuries to a 19-year-old who died in February.
There have been international calls on the Fiji military to stop human rights abuses.
Since the December coup, the military has used its power to question people at the barracks, bypassing conventional policing and judicial procedures.