Hours earlier, near Mladenovac - about 60 kilometres (37 miles) south of the capital - a 21-year-old gunman armed with an automatic weapon opened fire from a moving vehicle before fleeing, state-run RTS television reported.
"Two of the martyrs have completely distorted features due to the intensity of the shooting, which makes it difficult to identify them," the ministry said.
A string of high-profile hunger strikes during at least 13 stints in Israeli custody had turned Adnan into a national hero and revitalised hunger strikes as a form of protest among Palestinians incarcerated in Israeli jails.
Multiple nations have scrambled to evacuate embassy staff and citizens by road, air and sea from Sudan, where fighting between the army and paramilitaries has killed hundreds and led to acute shortages of water, food, medicines and fuel.
Ahmed Haroun said that he and other former officials of Bashir's government had left Kober prison and would take responsibility for their own protection, in a statement aired on Sudan's Tayba TV on Tuesday.
The Sudanese Armed Forces (SAF) and the Rapid Support Forces (RSF) agreed to the ceasefire "following intense negotiations", Secretary of State Antony Blinken said in a statement shortly before the truce took effect at midnight (2200 GMT Monday).
After international mediation, RSF commander Daglo, commonly known as Hemeti, said he would support a 24-hour "armistice", which the army denied any knowledge of before later blaming the RSF for breaking it.
Fighting between Sudan's army and the paramilitary RSF that erupted on Saturday has killed at least 185 people and injured more than 1,800, U.N. envoy Volker Perthes said.
