Police deputy director-general Al Adel Ajeb told Sudan Television that "the operation to recover bodies from the plane is going on now".
"It is a difficult operation because some bodies are completely burnt and there are body parts," he said.
A police official said that emergency services had rushed to the scene and managed to put out the blaze.
Al Jazeera's Imran Garda, reporting from Khartoum on Wednesday, said there were many conflicting reports on what exactly happened.
|At least 29 bodies have been pulled |
from the wreckage [EPA]
Police chief General Mohammad Najib earlier said bad weather had "caused the plane to crash land, split into two and catch fire".
At the time of the landing a sand storm in the Sudanese capital was restricting visibility, residents said.
But Yusuf Ibrahim, the director of Khartoum airport, said bad weather was not to blame and that the jet had landed safely and was about to park when an explosion happened on board.
Passengers who escaped the jet told Al Jazeera that the aircraft's right engine caught fire shortly after landing and the flames quickly spread.
The flight had arrived from the Jordanian capital Amman late on Tuesday.
In July 2003, 115 people were killed when a Sudan Airways Boeing 737 was destroyed after it caught fire while attempting to land at the Red Sea coast resort of Port Sudan.
Source: Al Jazeera and Agencies