It relates to an incident in which a man was stabbed in the stomach.
Detective Inspector David Hallaway said: “Police have arrested two men aged 23 and 29 on suspicion of attempted murder following a stabbing incident in Castlehill Gardens, Augher just after 11 pm last night, Thursday 21 May.
“A 40 year man sustained a stab wound to his stomach following an altercation in the street.
“His condition is described as being critical.
DI Hallaway continued, “ I appeal to anyone who was in the Castlehill Gardens area of Augher around 11 pm last night, witnessed the altercation or has any information they believe would assist us with our enquiries to contact detectives at Dungannon PSNI on the non emergency number 101 or alternatively crime stoppers on 0800 555 111.”