"We want the military council to be dissolved and be replaced by a civilian council having representatives of the army," said Mohamed Naji, a senior leader of the Sudanese Professionals Association, the group that launched the anti-Bashir campaign.
This civilian council should then make way for a four-year transitional civilian government, protest organisers say.
"It is increasingly clear that the revolution is still unfinished," Alan Boswell, an analyst with International Crisis Group told AFP.
"The security cabal which still has power in Sudan is clearly resisting demands that would force it to cede its own power."
He said protesters are not wrong when they say that those who took power in the military council are from the same ruling elite.
"That's not to say there hasn't been a change," Boswell said.
In addition to the departure of Bashir and his immediate successor Ibn Ouf, Salah Ghosh, the feared head of the National Intelligence and Security Service (NISS), has resigned.
He oversaw the crackdown on protesters that left more than 60 people dead, hundreds wounded and thousands jailed.
Now the reaction of the military council to the growing pressure from protesters and the international community looks set to be crucial.
"I don't think we are anywhere close to the end of the road yet," Boswell said.
"We are hitting pretty dangerous waters".
Both Western powers and the rest of Africa have pushed for greater change in Sudan.
The United States, United Kingdom and Norway have urged the military council to hold an "inclusive dialogue" to usher in civilian rule.
And the 55-member African Union on Monday threatened to suspend Sudan if the military fails to hand over power to civilians within 15 days.
The continental body said "a military-led transition would be completely contrary to the aspirations of the people of Sudan".
The military council has offered concessions to protesters, including sacking the prosecutor general as demanded.
But protesters, although singing and dancing in a festival-like atmosphere outside the sprawling military complex, remain clear about what they want.
"It's true that Bashir is the symbol of the regime, but I believe that we are still in the middle of the road," said Erij Salah, 23.
"We have to fight until we get rid of this regime."