There are unconfirmed reports that all four airmen aboard died in the crash.
The two planes were F4-fighter jets taking part in a training flight, according to the state news agency Anatolia.
The accident happened only hours after a Turkish RJ-100 airliner crashed near Diyarbakir in the same region, killing 75 people.
The cause of the mid-air collision is unknown, although Malatya province has been shrouded in the same thick fog which has covered Diyarbakir and is being blamed for Wednesday's commercial crash.
"You cannot see 10 meters (yards) ahead," an official from the office of the sub-governor of Akcadag town, near where the collision took place, told AFP.
The Turkish military has a heavy presence in the south-east of the country, having for many years battled an armed Kurdish uprising in the area.
Southern Turkey is also home to an airbase from which British and American planes patrol the northern no fly zone in Iraq.
There has been much speculation in recent weeks that Diyarbakir airport, a large airbase within easy reach of the Iraqi border, is one of the airfields the US would want to use in the event of an attack on Iraq.
Burnt beyond recognition
The passenger plane that crashed at Diyarbakir was a four-engine aircraft operated by Turkish Airlines.
It had been on an internal flight from Istanbul when it hit the ground 30 metres short of a military runway in the wrong part of the airport at about 2012 (1712 GMT) on Wednesday.
TURKISH AIR CRASHES
Turkish Airlines said there were about eight foreigners among the victims, including four Britons and one American.
The bodies were taken to a local university sports' hall, but identification is proving difficult as many of them were severely burnt.
The plane broke into three pieces and caught fire on impact, but five people survived the crash.
As news of the incident emerged, distraught relatives gathered at the airport to try to find out who had survived.
Many locals were so distressed that the police had trouble maintaining order as hysterical people took to the streets in sub-zero temperatures.
Black box recovered
The survivors include a woman, Aliye Il, who had a miraculous escape when she was thrown clear of the plane and landed on a bale of hay near the runway.
"I was thinking about unfastening my seat belt as we were about to land. Then a strong explosion rocked the plane and everyone and everything turned into balls of fire," she said.
The hay bale on which she landed subsequently burst into flames, but she managed to get up and flee to safety.
One of the two flight recorders, or "black boxes", has been recovered from the remains of the aircraft and is to be flown to Britain where its data will be analysed, Transport minister Binali Yildirim said.
The second black box has yet to be found and debris is reportedly scattered over an 800 square metres area.
The BBC correspondent in Turkey, Jonny Dymond, says it was the worst plane crash in Turkey for more than 25 years
It has prompted a furore in the Turkish press, which says that the absence of vital equipment for guiding incoming aircraft will have contributed to the crash.