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.
He was once seen as the most powerful person in the country after Bashir and protesters held him responsible for the killing of demonstrators demanding an end to military rule.
"We will continue. our sit-in until all our demands are met", including the formation of a fully civilian government, said one of the alliance's leaders, Omar al-Degier.
Protest organisers have given a list of demands to the country's new ruling military council that came to power after Bashir was removed from office.
The council demanded that the Sudanese military "step aside and hand over power to a transitional civilian-led political authority, in accordance with the will of the people and constitutional order, within a maximum period of fifteen days from the date of the adoption of the present communique [Monday]", according to the text. The SPA has also called for the confiscation of properties belonging to the ousted president's National Congress Party and the release of soldiers who sided with their movement.
"We urge Sudan's new leadership to take the steps necessary to build domestic and global support to help resolve Sudan's many pressing challenges", it said.
"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.
Meanwhile, the foreign ministry urged the worldwide community to back the military council "to achieve the Sudanese goal of democratic transition", it said in a statement.More news: London climate change protest
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The protesters, numbering about 5,000 with more arriving, chanted "Freedom, freedom" and "Revolution, revolution", and appealed to the army to protect them.
Siddiq also called for the "immediate reform" of Sudan's National Intelligence and Security Service (NISS).
"Afterwards, the SPA will be comprised of unions, and will be a guardian of democracy in Sudan", she added.
The sit-in outside the compound, which also includes the intelligence headquarters and the presidential residence, began on 6 April after more than three months of protests triggered by a deepening economic crisis.
"The decision whether to extradite [Bashir] to ICC will be made by a popularly elected government and not the transitional military council", military council member Jalaluddin Sheikh told journalists during a visit to the Ethiopian capital.
In a televised address to the nation, Sudan's then-Defence Minister, Lieutenant General Ahmed Awad Ibn Auf, announced that al-Bashir - who had seized power himself in a 1989 coup - had been arrested and taken to a "safe" location. The demonstrations against longtime leader al-Bashir led to his removal by the military last week.
Himeidti is also the head of Sudan's Rapid Support Forces (RSF), a paramilitary anti-insurgency force with its origins in the Janjaweed militias of the Darfur conflict. Sudan's government has previously denied wrongdoing by the RSF.
The deputy leader of Sudan's ruling military council, Lt. Gen. Mohamed Hamdan Daqlo, met in Khartoum on Sunday with USA charge d'affaires Steven Koutsis.