"We surely want our demands to be met, but both sides will have to be flexible to reach a deal," said a protester who spent the night at the army complex.
On Saturday, 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.
Burhan also pledged that individuals implicated in killing protesters would face justice and that protesters detained under a recent state of emergency would be freed.
Burhan took the oath of office on Friday after his predecessor General Awad Ibn Ouf stepped down just a day after the ouster of Bashir.
Tens of thousands of people have massed outside the army headquarters since April 6, initially to urge the armed forces to back their demand that Bashir be removed.
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.
Dozens of people have been killed in protest related violence since demonstrations erupted against Bashir's rule in December.