Hundreds of thousands took to the streets on Thursday in response to the killings.
Kabbashi spoke at a press conference following a night of negotiations with opposition groups over a constitutional declaration.
Sudan’s military council spokesman said on Friday that nine soldiers from the Rapid Support Forces (RSF) have been dismissed and detained in connection with recent violence in the cities of Omdurman and El-Obeid.
Lieutenant General Shams El Din Kabbashi added that the governor of North Kordofan state and its security council will be held accountable for the killing of six people including 4 school-children in the state capital El-Obeid on Monday.
Hundreds of thousands took to the streets on Thursday in response to the killings, and opposition medics said four protesters were killed and many injured by gunfire in Omdurman.
Kabbashi spoke at a press conference following a night of negotiations with opposition groups over a constitutional declaration, a document that would pave the way for a transitional government.
The two sides had signed a political deal in July setting a three-year transition period and a joint sovereign council, but talks over the constitutional declaration were called into question earlier this week.
African Union mediator for Sudan Mohamed Hassan Lebatt said the talks were set to continue on Friday night.