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.
The UN and 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 22:00 local time (20:00 GMT) to 04:00.
"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.
'A volatile and unpredictable situation'
This is a military coup with no clear roadmap for how the generals plan to hand over power to civilian rule.
The fear will be that they have no such intention. The security elite has calculated that removing Omar al-Bashir and imposing a curfew will buy them time and end the protests. If so this represents a serious miscalculation.
Sudanese Professionals Association (SPA) - which has spearheaded the demonstrations - and other civil society groups have made it clear they won't accept a cosmetic change. They have the numbers and are highly organised.
The military has the guns and the capacity for imposing brutal repression. But what then? A crackdown will not resolve the desperate economic crisis that brought years of simmering resentment on to the streets last December.
There is also the question of the cracks within the Sudanese security establishment, evident during the clashes between soldiers and intelligence/militia forces in recent days. It is a volatile and unpredictable situation that demands cool heads and compromise on the part of the military. The stability of Sudan depends on how they react to continued protests.
How did protesters react?
SPA said the military had announced a "coup" that would merely reproduce the same "faces and institutions that our great people revolted against".
It urged people to continue the sit-in outside the military complex - that began on Saturday - and to stay on the streets of cities across the country.
"Those who destroyed the country and killed the people are seeking to steal every drop of blood and sweat that the Sudanese people poured in their revolution that shook the throne of tyranny," the statement read.
SPA has previously said that any transitional administration must not include anyone from what it called the "tyrannical regime".
How did the protests begin?
Demonstration began in December. They were originally triggered by a rise in the cost of living, but crowds then began calling for the president to resign and his government to go.
Government officials said 38 people had died since December but Human Rights Watch said the number was higher.
In February, it looked as though the president might step down, but instead Mr Bashir declared a state of national emergency.
What international reaction has there been?
UN Secretary-General Antonio Guterres appealed for "calm and utmost restraint by all" and urged a transition that would meet the "democratic aspirations" of the people. UN Security Council is to discuss the situation in a closed-door meeting on Friday.
UK Foreign Secretary Jeremy Hunt said that a two-year military council was "not the answer".
"We need to see a swift move to an inclusive, representative, civilian leadership. And we need to ensure there's no more violence," he said on Twitter.
The US called on Sudan's military to bring civilians into the transitional government and said a two-year timeline was too long.
African Union condemned the military takeover. AU Commission chairperson Moussa Faki Mahamat said it was not an appropriate response to the challenges facing the country and the aspirations of its people.
Russia, which has twice hosted Mr Bashir, called for calm and said it was monitoring the situation.
Amnesty International's Secretary General Kumi Naidoo said that justice was "long overdue" for Mr Bashir.
"Omar al-Bashir is wanted for some of the most odious human rights violations of our generation and we need to finally see him held accountable," Mr Naidoo added.
Who is Omar al-Bashir?
Formerly an army officer, he seized power in a military coup in 1989.
His rule has been marked by civil war. The civil conflict with the south of the country ended in 2005 and South Sudan became independent in 2011.
Another civil conflict has been taking place in the western region of Darfur. Mr Bashir is accused of organising war crimes and crimes against humanity there by the ICC.
Despite an international arrest warrant issued by the ICC, he won consecutive elections in 2010 and 2015. However, his last victory was marred by a boycott by the main opposition parties.
The arrest warrant has led to an international travel ban. However, Mr Bashir has made diplomatic visits to Egypt, Saudi Arabia and South Africa.