The plane, which was on a training mission, crashed late on Thursday north of Omdurman, the twin city of the capital Khartoum on the west bank of the Nile.
"Two pilots who were on board were killed in the crash," said military spokesman Brigadier Ahmed Khalifa Shami in a statement released on Friday.
"The plane crashed after it had taken off for a training mission."
On Monday, a military helicopter had crashed in the war-torn region of Darfur as it was landing after a routine mission.
At least 17 killed in South Sudan plane crash
All passengers on board were rescued even as the helicopter caught fire, the army said, without giving any details of how many people were on board.
Most of Sudan's fleet consists of Russian-manufactured aircraft, and in recent years has suffered several crashes, with the military frequently blaming technical problems and bad weather.
In June 2017, four crew members on board a military helicopter were killed when it crashed in Northern State.
In April 2016, a Soviet-era Antonov An-26 transport plane crashed while landing in El Obeid, capital of North Kordofan state. All five crew members on board were killed.
Plane crash-lands in S.Sudan with 45 onboard: officials
In June 2013, two air force crew died when their helicopter crashed in war-torn Blue Nile state, just a week after one went down in South Kordofan state, another war zone.
The military has extensively used air power in its campaign against rebel groups in Blue Nile, South Kordofan and Darfur.
Rebels often claim to have shot down military aircraft in Sudan's conflict zones.
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