It wasn't immediately clear what caused the crash or whether any of the pilots attempted to eject.
An official from South Korea's Defence Ministry said crews were continuing to search for the pilots although the wreckage indicated they didn't survive. The official didn't want to be named, citing office rules.
The air force said in a statement that the pilots were flying back to their base in the city of Daegu after an unspecified mission. It said no civilian injury or property damage had so far been reported.
It took more than two hours for dozens of firefighters and rescuers to reach the wreckage deep into the mountain as they had to move on foot amid a thick fog, an official from the Chilgok Fire Department said.
An employee at a nearby golf club said he heard what seemed to be a succession of explosions that also left the club's building shaking.
"The fog was very thick and we couldn't see anything clearly," said the employee at the Gasan Country Club, who said the crash site was not far from the club's fourth hole. "There were several bangs that went off between gaps of a few seconds."
The employee also didn't want to be named, saying he wasn't authorised to speak to reporters.
