Large crowds have remained on the streets of the Sudanese capital, Khartoum, ignoring a night-time curfew declared by the country's new military council.
Long-time President Omar al-Bashir was overthrown and arrested on Thursday after months of street protests.
But demonstrators say the military council is part of the same regime.
The fresh stand-off has raised fears of a violent confrontation between protesters and the army.
There is also a real danger that different elements of the security forces and militia could turn their guns on each other, BBC World Service Africa editor Will Ross says.
The UN and the African Union have both issued calls for calm.
A mood of celebration that followed news of 75-year-old Mr Bashir's arrest quickly evaporated when organisers of the demonstrations called for a mass sit-in outside military headquarters to continue.
"This is a continuation of the same regime," said Sara Abdeljalil of the Sudanese Professionals Association. "So what we need to do is to continue the fight and the peaceful resistance."
Later, an official statement carried by state-run media said a curfew would run from 10pm to 4am.
"Citizens are advised to stick to it for their safety," it said, adding: "The armed forces and the security council will carry out its duty to uphold peace and security and protect citizens' livelihoods."
Crowds on the streets of Khartoum waved flags and chanted "Fall, again!" - refashioning their previous anti-Bashir slogan of "Fall, that's all!".
Mr Bashir is the subject of an international arrest warrant issued by the International Criminal Court (ICC), which accuses him of organising war crimes and crimes against humanity in Sudan's western Darfur region.
It is not clear what will happen to him now that he is in custody.
How did the coup unfold?
Early on Thursday, military vehicles entered the large compound in Khartoum housing the defence ministry, the army headquarters and Mr Bashir's personal residence.
State TV and radio interrupted programming and defence minister Awad Ibn Ouf announced "the toppling of the regime". He said Mr Bashir was being held "in a secure place" but did not give details.
Mr Ibn Ouf said the country had been suffering from "poor management, corruption, and an absence of justice" and he apologised "for the killing and violence that took place".
He said the army would oversee a two-year transitional period followed by elections.
The minister also said a three-month state of emergency was being put in place.
Sudan's constitution was being suspended, border crossings were being shut until further notice and airspace was being closed for 24 hours, he added.