His comments came after Sudan's army announced "the toppling of the regime", to be replaced by a transitional military council, but there was growing worldwide pressure for a handover to civilian rule.
Ouf, on a US sanctions list for Darfur genocide, was sworn in as head of the new military transitional council that has taken charge for the next two years.
Sudan's ousted president Omar al-Bashir, who is wanted by the International Criminal Court on charges of genocide and war crimes, will not be extradited, the country's new military rulers said Friday.
Zein Abedeen, who is on the military transitional council which took over after overthrowing al-Bashir on Thursday, also insisted the army has no ambition to hold the reins of power for long. Activists have demanded the military hand over power to a civilian government as soon as possible.
Sudan's military ousted President Omar al-Bashir hours earlier in response to almost four months of escalating popular protests in which dozens have been killed.
"The army announcement was disappointing", said another protester, Mohamed Ali.
Celebrations at al-Bashir's departure at the main Khartoum protest quickly shifted into calls for much broader reform.
Earlier on Friday, thousands of Sudanese demonstrators camped outside the defense ministry to push for a civilian government, defying a curfew and calling for mass prayers.
Amnesty has also called for the arrest of al-Bashir for human rights violations during his rule.
The 75-year-old, now under house arrest, becomes the second regional leader after Algeria's military-backed president, Abdelaziz Bouteflika, to leave this month in the face of nationwide protests.
Sudan President Bashir Ousted Amidst Military Coup
Escalating protests against al-Bashir's 30-year rule started in December and resulted in the killing of dozens. Mr Adawi is said to be favoured by regional neighbours at odds with Mr al-Bashir over his Islamist leanings.
Lieutenant General Abdel Fattah Abdelrahman Burhan will be the new head of the transitional military council, Ibn Auf said in a speech broadcast on state television on Friday.
Ousted Sudanese strongman Omar Al-Bashir.
He further announced the suspension of Sudan's 2005 Constitution and the dissolution of the Sudanese presidency, parliament and council of ministers.
"The Sudanese people should determine who leads them and their future and the Sudanese people have been clear and are demanding a civilian-led transition", Palladino said.
In the wake of the coup, worldwide human rights groups urged Sudanese military authorities to hand over the 75-year-old Bashir to the global Criminal Court, where he faces charges of war crimes, crimes against humanity and genocide for his deadly campaign against insurgents in the country's Darfur region.
Bashir's ouster comes only days after the same happened to his Algerian counterpart Abdelaziz Bouteflika who was equally forced to resign after intense protests and demonstrations.
Some protesters brought in mattresses, fans and even air conditioners, while others swept the streets to keep them clean, signalling they intend to stay long term.
The force draws its origins from the Janjaweed militias that were implicated in the Darfur genocide.
The African Union has criticised the military take-over in Sudan following the toppling of Omar al-Bashir.