The Sudanese Professionals Association (SPA), which has spearheaded protests that ended the three-decade rule of President Omar al-Bashir, renewed calls for the military transitional council to cede power to a civilian council with limited military representation.
The sit-in at the army headquarters in the capital, Khartoum, was the last straw that forced the military to oust President Omar al-Bashir last week.
Among the demands voiced during the press conference was the dismantling of Bashir's National Congress Party, the sacking of judiciary chiefs, dismissal of the general prosecutor and removal of the ruling military council. "We hope that everyone will head immediately to the areas of the sit-in to protect your revolution and your accomplishments", the SPA said.
At the news conference, the SPA said the military had promised to protect the sit-in.
On Monday, the group said in a statement on its Facebook page that protests will persist until there is the creation of a sovereign council, a mini transitional legislative council and a civil transitional government that can exercise wide executive powers.
Thousands remained encamped outside Khartoum's army headquarters to keep up pressure on a military council that took power after ousting Bashir on Thursday.
They were joined by the African Union, which threatened to suspend Sudan's membership unless civilian authority is in place within 15 days.
Earlier in the day, the SPA urged people into the streets, saying "There is an attempt to break up the sit-in".
In a televised speech, Burhan said the country's two-year transitional period will end with free and fair elections and vowed to put on trial those involved in the killing of the protesters as well as corruption under the old regime.
"We want to set up a civilian state based on freedom, justice and democracy", a council member, Lieutenant General Yasser al-Ata, told several political parties, urging them to agree on the figures to sit in civilian government.
A 10-member delegation representing the protesters had delivered a list of demands during talks with the council late on Saturday, according to a statement by the Alliance for Freedom and Change umbrella group.
Naji said that until the popular demands were met, protesters would resort to all peaceful means of opposition, including continuing their vigil in front of the army's headquarters.
Himeidti is also the head of Sudan's Rapid Support Forces (RSF), a paramilitary anti-insurgency force with its origins in the Janjaweed militias of the Darfur conflict.
"A military-led transition would be completely contrary to the aspirations of the people of Sudan", it said.
But the protesters' elation quickly turned to anger as Ibn Auf, a long-time al-Bashir loyalist, announced the establishment of a two-year transitional military council and later was sworn in as its head.
"Himeidti was part of the crimes that happened previously, but at least now he is on the side of the people", said Mohamed, a protester outside the army headquarters who gave only his first name for security reasons. In the latest shake-up, Burhan on Monday named Lieutenant General Hashim Abdelmotalib as the army's chief of staff.