Sudan's Defense Minister Awad Mohamed Ahmed Ibn Auf announced Thursday that al-Bashir had been arrested and the military council will take over the country for a two-year transitional period.
But the SPA said the military council was "not capable of creating change".
He says al-Bashir is in custody but declined to provide more details.
He said al-Bashir's top government members, including the vice president and associates, were also under arrest but again, didn't elaborate.
While addressing a news conference in the capital, Khartoum on Firday, Omar Zein Abideen said that the army has "no ambition to hold the reins of power", and stressed that "we are ready to step down as early as a month if a government is formed".
"This was not a coup", but a "tool of change", he said. "We came.to guide the country forward".
Thursday's announcement meant "we have not achieved anything", said one protester, who gave his name only as Adel.
So it was no surprise that after Mr Auf announced that the military had taken power for two years, had suspended the constitution and declared an emergency for three months, protesters vowed to stay put, defying a curfew announced by the usurpers.
The curfew and state of emergency have raised fears the military could eventually disperse the sit-in by force.
In Algeria, hopes among the protesters rose briefly last week when army chief Gen. Gaid Salah, responding to weeks of street protests, forced the ailing 82-year-old Bouteflika to step down from the presidency.
Separately, the military council's political committee chief, Lieutenant General Omar Zain al-Abdin, told diplomats Bashir's ouster after 30 years in power was "not a military coup".
At the sit-in, the mood was festive. The power of the people that brought down one of the longest serving despots in Africa is likely to send shivers throughout the rest of the Eastern and Horn of Africa region, whose people have been buckling under the misrule of strongmen, rigged elections and dwindling standard of living. Tens of thousands beat drums, sang and chanted slogans against the armed forces and Ibn Ouf after nightfall.
The U.S. State Department has called on the Sudanese military to "follow the will of the people" and "commit to the speedy handover to civilian rule".
United Nations chief Antonio Guterres called for a transition that would meet the "democratic aspirations" of the Sudanese people and appealed for "calm and utmost restraint by all", his spokesperson said.
The force draws its origins from the Janjaweed militias that were implicated in the Darfur genocide. China said it would continue to seek cooperation with Sudan regardless of the political situation.