Live ammunition has been used and eyewitnesses say there are fatalities.
Sudan has been governed by a Transitional Military Council (TMC) since President Omar al-Bashir was overthrown in a coup in April.
Protesters have been demanding that a civilian government should take over the running of the country.
The security services moved on the main protest site early on Monday.
Khartoum residents reported hearing heavy gunfire and seeing smoke rising from the area around the army headquarters.
At least five people are reported to have been killed and a number injured.
“Now an attempt is taking place to disperse the sit-in,” said a short statement from the Sudanese Professionals Association, the group which is spearheading nationwide protests.
The association also called for a campaign of “sweeping civil disobedience to topple the treacherous and killer military council and finalise our revolution”.
Protesters have been burning tyres and erecting barricades to try to fend off the security forces.
Journalist Benjamin Strick, who specialises in verifying footage on Twitter, has shared dramatic videos from Khartoum, where repeated gunfire could be heard.
Replying to @BenDoBrown
This is footage of University Street (شارع الجامعة) #Khartoum, in the background we can see the sit-in at Buri Rd. People are running and there is lots of gunfire. H/T to @ibr_2196 for 📹. The part of Buri Rd you can see is here: https://goo.gl/maps/LgE59NkxrGrjgrv26 … #اعتصام_القياده_العامه
Footage captured from livestream shows force used to enter sit-in. Many confimed gunshot wounds. Footage from Buri Rd in front of Navy HQ in #Khartoum, located here: https://goo.gl/maps/cdhMMc2a2kgpqGvC7 … H/T @EhabTheBeast #اعتصام_القياده_العامه #تسقط_بس #مجزرة_القيادة_العامة #SudanUprising pic.twitter.com/LbmdRzJqPQ
Sudan’s military has so far made no public comments.
The US embassy in Sudan said attacks by Sudanese security forces against protesters were “wrong and must stop”.
US Embassy Khartoum@USEmbassyKRT
Sudanese security forces’ attacks against protesters and other civilians is wrong and must stop. Responsibility falls on the TMC.