Shortly after taking off from Juba airport on Wednesday, the plane came down on the banks of the White Nile river, leaving a tail fin and lumps of fuselage strewn in vegetation close to the water.
Al Jazeera's Hiba Morgan, reporting from Juba, said bad weather was hampering the rescue effort.
"It is raining hard here in Juba, making it difficult to look for more victims. The cargo plane was carrying passengers and it is believed that many of them were not wearing seat belts."
In addition, he said an unknown number of people were killed on the ground as the Antonov plane crashed near where some fishermen were working. "We don't know the number of people that were killed on the ground," he added.
Radmir Gainanov, spokesman for Russia's diplomatic mission in Uganda, which also oversees South Sudan, said the embassy was in touch with local authorities, including the defense ministry.
"We are clarifying details," he told AFP news agency from Uganda.