Heavily armed members of the Rapid Support Forces are said to be fanning out across the capital and the neighbouring city of Omdurman, clearing barricades and firing into the air.
The military has faced international condemnation for the deadly crackdown on Monday. It has ended a pact with the protesters over a transition to civilian rule.
The two sides had initially agreed a three-year transition, culminating in elections. On Monday, however, the Transitional Military Council (TMC) said polls would be held within nine months.
The demonstrators had argued that a longer period was needed in order to guarantee fair elections and dismantle the political network associated with the former government of President Omar al-Bashir.
After 30 years in power, Bashir was overthrown by the military in April, amid pressure from the protesters.
The demonstrators had been occupying the square in front of the military headquarters since 6 April, five days before Bashir was overthrown.
Many Khartoum residents blamed the Rapid Support Forces for the crackdown. The paramilitary unit - formerly known as the Janjaweed - gained notoriety in the Darfur conflict in western Sudan, which began in 2003.
The protesters had called for the Islamic festival of Eid al-Fitr, marked on Tuesday and Wednesday this week, to be celebrated in the streets, as a gesture of defiance against the military.
On Tuesday, however, much of Khartoum seemed to be under lockdown. Video shot on mobile phones showed columns of troops advancing along the streets, removing barricades and firing into the air.
Flights into Khartoum have also been disrupted.
Large numbers of heavily armed troops were also reported on the streets of Omdurman, Sudan's second-largest city, just across the River Nile from Khartoum.
A woman, identified only as Sulaima, told the BBC that troops from the Rapid Support Forces were "all over Khartoum".
"They're surrounding neighbourhoods, they're threatening people. They're also using live ammunition. They're everywhere. We're not feeling safe and we don't have trust in the security forces. It's complete chaos."
Earlier, General Abdel Fattah al-Burhan, the TMC head, said on state television the council had decided to "stop negotiating" with the protesters and "cancel" all previous agreements, and that an election would be held in nine months.
The US, the UK and Norway expressed "serious concern" over the announcement, and called for "an agreed transfer of power to a civilian-led government".
( With inputs from IANS )