"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.
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.
Some members of the former government in Sudan have been arrested by the transitional military council which is now running the country, according to reports coming out of the country on Monday morning.
Sudan's military rulers faced pressure from demonstrators and Western governments to hand power to a new civilian government Monday as activists warned of an attempt to disperse a 10-day-old mass protest outside army headquarters.
The deputy leader also told the USA envoy how the military council would "preserve the security and stability of the country".
"Remember, we are talking about a regime that has been deep-rooted in power for 30 years, so the SPA and other powers behind this protest know. that the top ranks of the military, those who have staged this coup, will not easily give up the power that the military used to have in Sudan", Vall said. 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.
"This must be done credibly and swiftly, with protest leaders, political opposition, civil society organizations, and all relevant elements of society, including women".
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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.
Protest leaders say their demands include restructuring the country's feared NISS agency, whose chief Salih Ghosh resigned on Saturday.
On Sunday night, the council announced the appointment of Lieutenant General Abu Baker Mustafa as the new head of NISS in a televised announcement in which it also announced the sacking of Khartoum's envoy to Washington Mohamed Atta.
"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.
As former commander of the army's ground forces and inspector general of the army, Burhan oversaw the deployment of Sudanese troops to Yemen as part of the Saudi-led coalition.
But Qatar, which wielded some influence over Bashir's regime before Khartoum joined ranks with Riyadh in Yemen, has remained silent on the protests.