But the military council warned it would tolerate no breaches of security, after protesters defied a night-time curfew following Bashir's Thursday fall, keeping up their sit-outside the army headquarters.
Thousands of men and women, dressed in white, also braved the searing Sudanese heat on Friday to offer prayers outside the sprawling complex, witnesses said.
The imam leading the prayers was draped in the Sudanese flag.
Hussein Mohamed, an elderly man from Omdurman, said he was attending the protest for the first time in response to a call to hold Friday prayers there.
"It is too, too hot but I'm impressed by what our young men and women are doing here," he said. "I'll surely come again." Many Coptic Christians were also there, serving food and drinks to Muslims as they got ready for prayers.
Some also brought mats for the worshippers.
The army takeover brought to an end 30 years of rule by Bashir, one of Africa's longest serving leaders.
But Abdin said the council would never extradite him or any other Sudanese citizen.
The military council had announced a two-year transition period, but Sudan's UN envoy told the Security Council in New York that this could be shortened "depending on developments on the ground and agreements between stakeholders".
Protesters have held mass demonstrations for four months demanding Bashir's overthrow, defying repeated deadly attempts by riot police and the feared intelligence services to crush them.
But when his overthrow was finally announced on Thursday in an address to the nation, by Defence Minister Awad Ibnouf, it was met not with joy but anger.
Protest leaders have dismissed the transitional military council as the "same old faces" from the regime which led the country into multiple conflicts along with worsening poverty and social inequality.
Thursday's announcement meant "we have not achieved anything", said one protester who gave his name only as Adel.
"We will not stop our revolution. We are calling for the regime to step down, not only Bashir." Analysts said Bashir's overthrow in a "palace coup" made the transition to democracy in Sudan a more distant prospect.
"Ironically, the prospects for democratic transition may be more remote than when Bashir was in power, as there's no centre of power with which to negotiate," said Alex de Waal, a Sudan specialist at Tufts University.
"The power struggle within the security cabal that took power yesterday is just beginning," de Waal said. "Bashir had kept their rivalries and ambitions in check; his removal brings in its wake an unregulated uncertainty."
Protesters at the sit-in said their quarrel was with the commanders who had led the coup, not the rank and file.
"This is now our square. We have taken it and won't leave until victory is achieved," said one protester who gave his name as Abu Obeida.
"We broke the curfew. We will continue doing it until we have a civilian transitional government." Multiple world powers have made calls for a peaceful transition.
Washington urged the military council "to exercise restraint and to allow space for civilian participation within the government".
The European Union urged the army to carry out a "swift" handover to civilian rule. The African Union decried Bashir's military overthrow, saying it was "not the appropriate response to the challenges facing Sudan and the aspirations of its people".
Most shops and offices were closed on Friday, a day of prayer and rest in Sudan. But crowds again began thronging the streets of Khartoum after the main weekly Islamic prayers, raising fears of a confrontation between protesters and the security forces.
The ousted president stands accused of unleashing Arab militias in a scorched earth campaign against minority villages, killing tens of thousands of civilians and forcing hundreds of thousands more into camps.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)