On Sunday the organisation which spearheaded the protests against Bashir, the Sudanese Professionals Association, called on the military council "to immediately transfer power to a civilian government".
"The Sudanese Professionals Association calls on its supporters to continue with the sit-in until the revolution achieves its demands," it added.
Earlier the military council met with political parties and urged them to agree on an "independent figure" to be the country's prime minister, an AFP correspondent present at the meeting said.
"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.
The protesters have insisted civilian representatives must join the military council.
A 10-member delegation representing the protesters delivered their demands during talks with the council late Saturday, according to a statement by the Alliance for Freedom and Change umbrella group spearheading the rallies.
The foreign ministry urged the international community to back the military council "to achieve the Sudanese goal of democratic transition," it said in a statement.
Talks between protest leaders and Sudan's new rulers were followed Sunday by a meeting between Washington's top envoy to Khartoum, Steven Koutsis, and the military council's deputy.
Mohammad Hamdan Daglo, widely known as Himeidti, told Koutsis "about the measures taken by the military council to preserve the security and stability of the country," the official SUNA news agency reported.
On Saturday, the military council's new chief General Burhan vowed to dismantle Bashir's regime, lifting a night-time curfew with immediate effect.
He also pledged that individuals implicated in killing protesters would face justice and that protesters detained under a state of emergency imposed by Bashir during his final weeks in power would be freed.
Burhan took the oath of office on Friday after his predecessor General Awad Ibn Ouf stepped down little more than 24 hours after Bashir's ouster.
Tens of thousands of people have massed non-stop outside the army headquarters since April 6, initially to urge the military to back their demand that Bashir be removed. Burhan comes with less baggage from Bashir's deeply unpopular rule than Ibn Ouf, a former defence minister and long-time close aide of the deposed president.
But while celebrating the fall of both men in quick succession, protesters remain cautious.
Protest leaders say their demands include restructuring the country's feared NISS agency, whose chief Salih Ghosh resigned on Saturday.
Rights group Amnesty International on Saturday urged the military council to examine the actions of Ghosh during a crackdown against protesters during the final weeks of Bashir's rule.
The newly formed 10-member transitional council contains several faces from Bashir's regime.
"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.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)