The protests, which erupted in December, have become the biggest challenge yet to Bashir's three decades of iron-fisted rule.
Thursday marked the sixth day of a defiant sit-in outside the military's headquarters, which also houses Bashir's official residence and the defence ministry.
Crowds of demonstrators have spent five nights thronging the sprawling complex, singing and dancing to the tunes of revolutionary songs.
Several military vehicles carrying troops entered the army compound in the early hours of Thursday, witnesses said.
"People are coming in droves," said an onlooker at the sit-in without revealing his name for security reasons.
The group spearheading the nationwide demonstrations urged residents of the capital to mass outside army headquarters.
"We call on our people from across the Khartoum capital and the region around to immediately go to the sit-in area and not leave from there until our next statement is issued," the Sudanese Professionals Association said.
The demonstrators have braved repeated volleys of tear gas from members of the powerful National Intelligence and Security Service (NISS) since they began camping outside the complex on April 6, protest organisers say.
But for the first time on Tuesday night they did not face any "threat" from security agents, said a protester who requested anonymity for security reasons.
That came after 11 people, including six members of the security forces, were killed on Tuesday during demonstrations in the capital, government spokesman Hassan Ismail told the official SUNA news agency.
Officials say 49 people have died in protest-related violence since demonstrations first erupted in December.
"I hope our revolution will achieve its goal," said Alaa Salah, dubbed the protest movement's "Nubian queen", referring to an ancient name for Sudan, after a video clip went viral of her conducting chants with demonstrators outside the army headquarters.
Earlier this week, the US, Britain and Norway for the first time threw their weight behind the protesters.
"The time has come for the Sudanese authorities to respond to these popular demands in a serious" way, the countries' Khartoum embassies said in a statement.
"The Sudanese authorities must now respond and deliver a credible plan for this political transition." Sudan, along with Iran, Syria and North Korea, is on Washington's blacklist of state sponsors of terrorism.
On Tuesday, security agents had to abort bids to disperse the crowds when soldiers countered their volleys of tear gas by firing in the air, witnesses said.
NISS said it was "monitoring the demonstrations and discharging its duty according to law".
Sudan's police has ordered its forces not to intervene against protesters.
"We call on God to preserve the security and calm of our country... and to unite the Sudanese people... for an agreement which would support the peaceful transition of power," it said in a statement.
On Wednesday, protesters were raising funds to ensure a regular supply of food and water for the crowd.
"Many shop owners and businessmen have offered us free supplies," said one demonstrator.
Protesters have set up five big screens at the complex to watch football matches, an onlooker said.
Witnesses said troops stationed vehicles mounted with machine-guns at the gates of the army complex.
The SPA said "several members and leaders" of Sudan's paramilitary Rapid Support Force (RSF) had given indications they would join the movement.
TheF is made up of Arab militias that fought on the side of government forces against rebels in Sudan's western region of Darfur in the initial years of the conflict.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)