But for angry protesters, the same regime remained in place, and since the announcement, they have turned their anger on the council and its newly appointed chief Ibn Ouf.
Burhan said the Transitional Military Council invites political parties, the opposition and NGOs to deal with the current situation "with cooperation and understanding", adding that a civilian government will be formed after consultations.
George Clooney says overthrowing Sudan's autocratic president doesn't go far enough and has called for "dismantling" the system that kept Omar al-Bashir in power for 30 years.
They refused to leave the streets, saying the coup leaders were too close to Bashir.
Lt-Gen Abdel Fattah al-Burhan announced the "restructuring of state institutions", in a televised address.
Following the military coup on Thursday, which ended the 30-year rule of Al-Bashir, many felt that the ouster had exposed him to arrest by ICC, after the being deprived the office that gave him immunity for over a decade.
The European Union urged the army to carry out a "swift" handover to civilian rule while United Nations chief UN chief Antonio Guterres called for a transition that would meet the "democratic aspirations" of the Sudanese people.
"The chief of the Transitional Military Council, Abdel Fattah al-Burhan, has accepted the resignation of. the chief of NISS", the Transitional Military Council said.
"Until these demands are fully met, we must continue with our sit-in at the General Command of the Armed Forces", the SPA said.
In an updated travel advisory, the department said "violent crime such as kidnapping, armed robbery, home invasion and carjacking is common" and warned citizens not to travel to Sudan. Military officials say he is under house arrest in the capital, Khartoum, and will be tried for unspecified crimes by Sudanese courts.
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Alsadig Almahdi, the last civilian prime minister before Bashir seized power in 1989 and a great-grandson of the Mahdi who led the uprising against British rule in the 1880s, oversaw Friday prayers at the protest site.
Lieutenant General Omar Zein Abedeen, head of the political military committee, promised to serve as the "protectors" of public will.
That came after the African Union decried Bashir's military ouster, saying it was "not the appropriate response to the challenges facing Sudan and the aspirations of its people". "We are calling for the regime to step down, not only Bashir".
On Friday, hours before he was named as Sudan's new military ruler, he was seen talking to protesters who have camped outside the army headquarters since 6 April.
Earlier, the main protest organising group rejected the transitional military council's promise to set up a civilian government and hand over power to an elected president within two years.
Sudan's intelligence service said it was freeing all political prisoners.
Last month, Middle East Eye revealed that Gosh had held secret talks with the head of Mossad in Germany in February as part of a plot hatched by Israel's Gulf allies to elevate him to the presidency if Bashir was toppled from power.
Leading protest group, the Sudanese Professionals' Association, issued a statement rejecting the military's declaration, claiming its intervention "reproduced the same faces and institutions that our courageous people have revolted against". "The maximum is two years", he said.
"At the same time, they don't want to do anything that would encourage other protests that would take their inspiration from recent events in Algeria and Sudan", he said.