One passenger said the plane had tried to land at Khartoum airport "but then the captain told us we couldn't land because of bad weather".
He said the plane then flew to the Red Sea city of Port Sudan before returning to Khartoum an hour later.
"When (the pilot) tried to land there was a crash," the passenger told Sudan Television.
Another survivor, Al Haj Bashir, said the landing in Khartoum was "not normal" and that there was "an explosion in the right wing" two or three minutes after the plane landed.
A mortuary near Khartoum airport said it had received 28 bodies. Youssef Mukhtar, a doctor who visited the mortuary early on Wednesday said: "They expect more."
At its height the fire appeared to be consuming the fuselage and cockpit area. The emergency crews eventually managed to extinguish the blaze.
Television pictures showed emergency escape chutes at the side of the blazing aircraft and ambulances on the tarmac.
A spokesman for Sudan's civil aviation authorities said all but one of the crew had been found alive.
"The task of counting the survivors has been complicated because in the alarm and confusion they dispersed and some of them seem to have left the airport area," said the spokesman.
"Whether (the fire was due to) a technical reason we don't know yet," airport director Yusuf Ibrahim told Sudanese TV.
"The plane was coming from Amman and Syria ... It landed safely at Khartoum airport and they talked to the control tower which told them where to taxi. At this moment an explosion happened," he said.
Five years ago, a Sudan Airways Boeing 737 crashed shortly after takeoff near Port Sudan, killing 104 passengers and the crew of 11.
