Payton Knopf, an analyst at the United States Institute for Peace, called for an global consensus on a civilian-led transition in Sudan, warning that failure to do so could lead to "chaos" in the country.
But within minutes of the announcement of the two-year military council, many protest leaders said the demonstrations would continue.
General Awad Mohamed Ahmed Ibn Auf, set to lead a two-year transitional government, before paving way for an election.
Ouf also said the government and the presidency have been dissolved, and imposed a night curfew.
Egypt expressed its "complete support" Thursday for the Sudanese people and their army in the political transition to come, following the ouster of long-time autocrat Omar al-Bashir.
Protester Hiba Ali told the BBC that "the suspense is killing" as she and others waited for the military to tell them what was happening.
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Mahamat also called for all parties to exercise calm and utmost restraint and to respect the rights of citizens, foreign nationals and private property.
The leading protest group, the Association of Sudanese Professionals, said power had to be handed over to a civilian transitional government made up of people who had no links to the "tyrannical regime". The 75-year-old becomes the second regional leader after Algerian President Abdelaziz Bouteflika to leave this month in the face of nationwide protests, stirring echoes of the Arab Spring uprisings that rocked the region from 2011.
Protesters also attacked the offices of Sudan's intelligence and security service in the eastern cities of Port Sudan and Kassala on Thursday, witnesses said.
Thursday's brief statement by the National Security and Intelligence service did not indicate when the release would take place.
A prominent exiled Sudanese cartoonist drew a caricature of al-Bashir sitting on a throne, with one of its broken legs replaced by a brick. The activists spoke on condition of anonymity for fear of reprisal.
Shortly afterward, thousands of demonstrators packed the streets of central Khartoum, their mood turning from jubilation at Mr al-Bashir's expected departure to anger at the announcement of a military-led transition, a Reuters witness said.
"The Embassy is aware of reports of a military takeover of the Government", the State Department said. They accused his government of failing to deal with the economy.
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All of #Sudan is waiting to hear the army announcement after five days of a sit-in at the military headquarters.
The officials declined to elaborate.
As a young officer, al-Bashir was groomed and trusted by the Islamist movement, which played a key role in propping him up for years.
Sudanese Defence Minister Awad Ibn Auf said in a hotly anticipated press statement that the army was "sorry for the loss of life amongst civilians" during the protests calling for Al-Bashir's removal; which government figure place at 32.
The situation in Khartoum remains fluid and it wasn't immediately possible to confirm that al-Bashir is being ousted.
Tens of thousands of Sudanese were on the streets of the capital, Khartoum. They spoke on condition of anonymity because they were not authorized to talk to the media.
The announcement raised expectations the statement Thursday could address almost four months of anti-government protests demanding that longtime President Omar al-Bashir step down and could be a sign that he is relinquishing power.
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Meanwhile, the movement called on protesters to keep up the pressure by continuing their main sit-in outside the military's headquarters in Khartoum.