Salah Gosh, the head of Sudan's feared National Intelligence and Security Service (NISS), has resigned from his post, the country's new military rulers have said on Saturday.
The military council under Ibn Auf had said it would not extradite Bashir to face accusations of genocide at the worldwide war crimes court.
Sudanese forces celebrate after officials said the military had forced longtime autocratic President Omar al-Bashir to step down after 30 years in power in Khartoum, Sudan.
"He's never been in the limelight like Ibn Ouf or General Kamal Abdelmarouf", the officer said, referring to the army's former chief of staff.
Ghosh had overseen a sweeping crackdown led by NISS agents against protesters taking part in four months of mass demonstrations that led to the toppling of Bashir in a palace coup by the army on Thursday.
"God willing, the government will be completely civilian..."More news: NYC's New Policy on Measles Vaccine Prompts Renewed Focus in NJ
But coup group warned it would tolerate "no breaches of security" after protesters defied a night-time curfew to keep up a sit-in demanding immediate civilian rule.
General Awad Ibn Ouf also announced his successor, army General Abdel-Fattah Burhan, general inspector of the armed forces, as head of the transitional council.
Omar el-Digeir, leader of the opposition Sudanese Congress Party, said the military should not be "the sole custodians of power". China said it would continue to seek cooperation with Sudan regardless of the political situation.
Despite enabling the ouster of Bashir, the new administration falls short of the demand for a civilian transition government which protesters, stung by three decades of worsening economy and authoritarian rule, had called for. The head of the military council's political committee, Omar Zain al-Abideen, said the council would hold a dialogue with political entities.
In March 2009, ICC slapped Al-Bashir with the first warrant of arrest on five counts of crimes against humanity in Darfur, where his troops quelled a rebellion in 2013.
"The new government authorities of Sudan must surrender al-Bashir, as well as Ahmad Muhammad Harun, Ali Muhammad Ali Abd-Al-Rahman (Ali Kushayb"), Abdel Raheem Muhammad Hussein, and Abdallah Banda Abakaer Nourain to the ICC in order to provide justice to the victims of the global crimes and the other perpetrators of the human right violations that have been committed in the country.More news: Trump Administration Rejects MLB/Cuba Posting Agreement
Organisers of the protests that have rocked Sudan since December vowed to press on until the whole regime was swept aside. People chanted: "The second has fallen!" a reference to Ibn Auf and Bashir, witnesses said.
At least 16 people have been killed by stray bullets at the protests since Thursday, police say.
He further asserted that the military statement was nothing but an effort to duplicate Bashir's regime.
Thousands of protestors heeded the call to stage a sit-in outside Khartoum army headquarters in defiance of the curfew as pressure piled on the military council 's to hand over to civilian rule.
However, the military council has said it will not extradite Mr Bashir, who denies the charges, although he may be put on trial in Sudan.
General Awad Ibn Aufannounced that Bashir had been arrested and a military-led transitional government will rule for two years.More news: Attorney General Barr tells Congress that 'spying' on Trump campaign 'did occur'
World powers, including the United States and Britain, said they supported a peaceful and democratic transition sooner than two years.