The aeroplane, which had been carrying 214 people, burst into flames after landing on Tuesday night.
Thirty bodies have been taken to Khartoum's morgue, Abdin said.
Earlier state television had reported that nearly half of the 203 passengers were killed when the plane burst into flames after one of its engines exploded on landing.
The plane was carrying 11 crew.
Investigation under way
The civil aviation authority and Sudan Airways were investigating the cause of the accident amid contradictory reports that the fire was caused by either the weather or a technical failure.
Airport authorities said an engine caught fire, spreading to the fuselage, while survivors said weather conditions at the time of the landing were poor, with the capital hit by a sandstorm and then heavy showers.
The aeroplane, which had been carrying 214
people, burst into flames after landing [AFP]
"There was an explosion in one of the engines and the plane caught fire," Yussef Ibrahim, the airport director,  said.
He told Sudanese television that "all measures had been taken to return airport activity and flights back to normal" and that domestic and international flights have resumed.
Mabruk Mubarak Salim, Sudan's state transport minister, said on Tuesday: "Today's weather is one of the main reasons for what happened".
El-Sheikh el-Faki, a civil aviation official, said that the plane "landed okay and then it skidded and caught fire", according to the AFP news agency.
The plane had flown from Amman via Damascus. It was turned back once from Khartoum by bad weather and forced to land in Port Sudan, before being allowed to return to Khartoum, Suna, Sudan's official news agency said.
TV pictures on Tuesday showed flames tearing through the upper section of the fuselage hours after the fire broke out.
An emergency escape slide could be seen attached to one of the central doors of the plane.