It's understood the man -- named locally as Aloysius Hackett -- was found dead outside his home in the Aghindarragh Road area on Friday night.
Detectives are continuing to question an 18-year-old man who was arrested at the scene.
Reacting to the death, Fermanagh and South Tyrone MLA Tom Elliott said: "While the police are obviously investigating the circumstances around this death it is clearly a very difficult time for the family and wider community.
"I trust the police can develop their investigations at an early stage and establish the facts of the case.
"Augher is a close knit rural community where an incident like this will have a bearing on the general population of the area."
Stormont Minister and Fermanagh and South Tyrone MLA, Arlene Foster, said her thoughts were with with deceased's family.
She described the death as a "tragedy" and "incredibly sad."