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.
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, Mr 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 Mr 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.
Sudan's military has faced international condemnation for its attack, but there were signs it could have happened. The country has been driven backwards by a military elite intent on holding on to power.
The TMC has scrapped agreements reached with the opposition Forces of Freedom and Change (FFC), saying this will speed up the transition to democratic elections. That plan is likely a fiction.
The military also enjoys another advantage: in an age of international division, the notion of an "international community" pressuring the regime is fantasy. Sudan's crisis has exposed the reality of international politics: that force can have its way, without consequence, if the killers and torturers represent a valuable asset to other powers.
It is impossible to say whether the FFC can come back as a street-driven force. What will not change, in fact what has been deepened, is the alienation of people from their rulers.
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, Gen 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".
What happened on Monday?
The security services moved on the main protest site early on Monday and, according to activists, forces also surrounded a hospital in Khartoum and opened fire at another.
In a statement read on national television, the military council said the operation had targeted "trouble makers and petty criminals" and that they were dedicated to protecting civilians.
The Sudanese Professionals Association (SPA), which is spearheading the nationwide protests, responded by calling for a campaign of "sweeping civil disobedience to topple the treacherous and killer military council".