The Antonov aircraft crashed on Tuesday over a populated district in the city of Omdurman, also injuring at least 10 people, according to the government-run Khartoum Media Office.
The military said the plane crashed while taking off from the Wadi Sayidna air base north of Omdurman, which is the sister city of the capital, Khartoum.
The crash also damaged a number of houses in the Karrari district of Omdurman, the media office said.
The military earlier said that armed forces personnel and civilians were killed in the crash, but did not provide figures.
It did not say what caused the crash.
The health ministry said some bodies were transferred to the Nau hospital in Omdurman.
Local media reported that the aircraft was on the way to the Red Sea city of Port Sudan, the seat of the military-backed government, when it crashed over the Al-Thawra neighbourhood in the Karrari district.
Residents reported loud explosions from the crash, which sent thick clouds of smoke and dust over Omdurman.
The aircraft was carrying high-ranking military officers, according to the Sudan Tribune news outlet.
But the military has not confirmed that.
Aircraft crashes are common in Sudan, mostly because of the country's poor aviation safety record.
In 2020, at least 16 people were killed when a military plane, a Russian Antonov An-12, crashed in the western region of Darfur.
In 2003, a civilian Sudan Airways plane crashed into a hillside while trying to make an emergency landing, killing 116 people, including eight foreigners.
Only a boy survived the crash.
Sudan has been in a state of civil war since 2023 when tensions between the military and a notorious paramilitary group, the Rapid Support Forces, exploded into open warfare.
The fighting has wrecked urban areas and has been marked by atrocities, including mass rape and ethnically motivated killings, that amount to war crimes and crimes against humanity, especially in the western region of Darfur, according to the United Nations and international rights groups.
The war has intensified in recent months, with the military making steady advances against the RSF in Khartoum and elsewhere in the country.
The RSF, which controls most of Darfur, said it downed a military aircraft on Monday in Nyala, the provincial capital of South Darfur province.
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