One of the five survivors told of falling from the plane after it split apart on impact and landing in a pile of hay.
"The plane split in two and was burning. Then there was an explosion.... The whole plane was burning," Aliye Il told the Anatolia news agency.
She said the haystack that cushioned her fall then caught fire, forcing her to run for safety. Anatolia did not give the woman's age.
While Transport Minister Binali Yildirim said there was heavy fog at the time of the crash at Diyarbakir airport, 635 miles southeast of Istanbul, he said the precise cause would not be known until the plane's flight data and cockpit voice recorders were recovered.
The four-engine British Aerospace RJ 100 jet hit the ground 40 yards short of the runway in the military section of the dual-use airport at Diyarbakir, a largely Kurdish city 75 miles north of the Syrian border.
Interior Minister Abdulkadir Aksu said 72 people died. He told NTV television soldiers helped evacuate the injured.
As relatives of passengers crowed the airport for news of loved ones, Diyarbakir Governor Ahmet Cemil Serhadli reported the fire caused by the crash had been extinguished.
The five injured were taken to Diyarbakir's central hospital and CNN-Turk television said they were in shock but had no life threatening injuries. There were no reports of injuries among people on the ground.
Last week, several flights to Diyarbakir were canceled because of bad weather.
In November, a Russian small plane carrying 28 people crashed near an airport in the Turkish Mediterranean resort of Antalya after it clipped a power line. No one was killed.
In May 2001, a military transport plane crashed in southeastern Turkey, killing 34 officers and soldiers from Turkey's elite special forces.
A civilian jetliner crashed in eastern Turkey in 1991, killing 55 people after the pilot insisted on landing despite a snowstorm that drastically cut visibility.