The chief of the military council General Abdel Fattah al-Burhan vowed to dismantle Bashir's regime, and he lifted a night time curfew with immediate effect.
On Thursday the army toppled the veteran leader, who had swept to power in an Islamist-backed coup in 1989.
But the protesters have vowed to remain in place until the military council demonstrably accepts its demands.
Sudanese protest organisers presented demands including the creation of a civilian government in talks with the country's new military rulers late Saturday, the group spearheading demonstrations said.
Thousands remained encamped outside the army headquarters in the capital overnight to keep up the pressure on a military council that took power after ousting veteran leader Omar al-Bashir on Thursday.
A 10-member delegation representing the protesters held talks with the military council and delivered their demands on Saturday, according to a statement by the umbrella group leading the protests, the Alliance for Freedom and Change.
One of the alliance's leaders, Omar al-Degier, said in the statement that the demands include restructuring the country's feared National Intelligence and Security Service (NISS), whose chief Salih Ghosh has resigned following the ouster of Bashir.
"We will continue... our sit-in until all our demands are met," including the formation of a fully civilian government, Degier said.
The Alliance for Freedom and Change insists that civilian representatives should be accepted onto the military council, and that a fully civilian government should be formed to run daily administration.