The statement comes nearly a week since the Sudanese military deposed President Omar al-Bashir, who had held power for 30 years, on April 11 following months of peaceful protests that brought the country to a standstill.
Earlier on Monday, Sudan's military attempted to break up an anti-government sit-in outside its headquarters in the capital Khartoum, but the protesters blocked the attempt.
"We call on our people to come immediately to the sit-in area to protect our revolution", the SPA said in a statement, without saying who was responsible.
Also on Sunday, the military council said it had arrested members of the former government and vowed to leave protests alone while stating that the former ruling National Congress party would be barred from participating in the interim government.
On Sunday, the military council said it would name a civilian prime minister and Cabinet to help run the country but would not name a civilian to the office of the president.
The African Union meanwhile gave Sudan's military 15 days to hand over power to a "civilian-led political authority" or face suspension from the union's activities.
The military council later held a press conference at which its spokesperson did not respond to the protesters' latest demands.
"It is time for the transitional military council and all other parties to enter into an inclusive dialogue to effect a transition to civilian rule", they said.
"We want to set up a civilian state based on freedom, justice and democracy", a council member, Lieutenant General Yasser al-Ata, told several political parties, urging them to agree on the figures to sit in civilian government.
When the military announced Bashir's ousting, they said he had been arrested and was being kept at a "safe place".
A 10-member delegation representing the protesters delivered their demands during talks with the council late on Saturday, according to a statement by the Alliance for Freedom and Change umbrella group spearheading the rallies.
As part of the shake-up at the top, a new NISS head and army chief of staff have been appointed.
Dagalo, known by his nickname Hemedti, heads Sudan's Rapid Support Forces (RSF), which human rights groups have accused of widespread abuses in the western region of Darfur. But at the protest site Monday, witnesses said demonstrators put up a banner with a photograph of Himeidti which read: "We will not forget that you stood with us".
Al Jazeera's Mohamed Vall, reporting from Khartoum, said the recent concessions by Sudan's military rulers had failed to win over protesters, many of whom remain distrustful of the higher echelons of the country's armed forces due to their historical links to al-Bashir's former administration. The demonstrations against longtime leader al-Bashir led to his removal by the military last week. He also ordered the release of all prisoners jailed under emergency laws ordered by the ousted president.
It said council chief General Abdel Fattah al-Burhan was "committed to having a complete civilian government and the role of the council will be to maintain the sovereignty of the country".