Previous attempts to break up the sit-in before al-Bashir's ouster last Thursday killed dozens of people.
Below are their key demands, which the umbrella group Alliance for Freedom and Change says must to be met for the sit-in to end.
"We want to set up a civilian state based on freedom, justice and democracy", a council member, Lieutenant General Yasser al-Ata, told members of several political parties.
A new interim civilian body should be given full executive powers, with the armed forces having representation, and the Transitional Military Council (TMC) that took over last week should be dissolved, the SPA said.
What's the solution to the unrest and what should we expect of the new regime?
Also Monday, Gen. Abdel-Fattah Burhan, the head of the transitional military council, announced an overhaul of the military leadership and appointed a new chief of staff, according to a military statement.
The military council's deputy Himeidti is a field commander for the Rapid Support Forces (RSF) counter-insurgency unit, which rights groups have accused of abuses in Darfur.
"For us in the SPA, in the first stage, the transitional government stage, we will play a role in the restoration of the civil service and state institutions and establishing a democratic state", said Gamaria Omar, an SPA member. Tens of thousands of people have massed non-stop outside the army headquarters since April 6, initially urging the military to back their demand for Bashir's removal.
Sudanese military forced to abandon attempt to clear protesters
Al-Bashir, who came to power in an Islamist coup in 1989, imposed a nationwide state of emergency February 22 in an attempt to suppress the protests after an initial crackdown failed.
Burhan comes with less baggage from Bashir's deeply unpopular rule than Ibn Ouf, a former defence minister and longtime close aide of the deposed president.
Protest leaders have called for the feared intelligence agency, whose chief Salah Gosh resigned on Saturday, to be restructured and for NISS officials to face prosecution.
Hemedti has also met with other Western diplomats, including the US chargé d'affaires and Dutch ambassador to Sudan.
"The objectives of the revolution can not be achieved totally and completely in the face of the backstage manipulations by the remnants of the regime", SPA member Taha Osman told reporters in the capital, Khartoum.
On Saturday evening, the new military ruler named NISS deputy head Jalaluddin Sheikh to the council, with Himeidti as its deputy head.
The TMC's deputy head, Mohamed Hamdan Dagalo, commonly known by his nickname Hemedti, said on Monday the Sudanese forces participating in the Saudi-led coalition fighting Iran-aligned Houthis in Yemen will remain there, SUNA said.
The gas-rich country is locked in a almost two-year-old diplomatic standoff with Saudi Arabia, the UAE, Bahrain and Egypt.
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