It is understood a group of boys were swimming at the quarry, at about 18:00 on Saturday 1st June.
Police divers, the Fire and Rescue Service and the coastguard were involved in efforts to save the two men. The quarry is close to Spence mountain, between Newcastle and Annalong.
Cllr Patrick Clarke stated: “I am deeply saddened that the lives of two people have been lost in such very tragic circumstances at the disused quarry.
“There is a deep sense of loss and shock in the local community.
“I would like to commend the efforts of the PSNI divers, the Fire and Rescue Service, and the coastguard who were involved in trying to rescue both men.
“This is an awful tragedy and my heartfelt sympathies go out to the families of Kevin O’Hare and Colin Polland.”