Mohamed Hassan Lebatt also called for the ruling military council and opposition coalition to sign a constitutional declaration they have been wrangling over for weeks.
A joint legal committee from both sides is due to meet later on Wednesday, when it is expected to complete its work on the document, he told a news conference.
A date will be set for signing the constitutional declaration after the meeting, he said, adding he hoped that would happen quickly, Reuters reported.
Six people, at least four of whom were children, were shot dead on Monday when security forces broke up a student protest in El-Obeid, 400 km (250 miles) southwest of Khartoum, opposition-linked doctors said. The teenagers were rallying against fuel and bread shortages, residents said.
The children's deaths came at a time of heightened tension between Sudan's military rulers and the main opposition coalition, and delayed already stalled talks over a transition deal following the overthrow of long-time ruler Omar al-Bashir.