CAIRO — Sudan’s new ruling military council announced on Sunday that it would name a civilian prime minister and cabinet, but not a president, to help govern the country after the coup that removed the longtime leader Omar Hassan al-Bashir.

An army spokesman, Lt. Gen. Shamseldin Kibashi, also said in televised remarks that the military had begun to overhaul security organizations and would allow demonstrations to continue outside the military headquarters in Khartoum, the capital.

The statement came after a second day of meetings between the army and organizers of the months of escalating protests that led to Mr. al-Bashir’s ouster on Thursday.

The announcement was unlikely to satisfy protesters, though, who have demanded full civilian rule. Organizers have urged the military to “immediately and unconditionally” hand power to a transitional civilian government.