Prime Minister Abdalla Hamdok tells a group of political and intellectual figures that he will step down, Reuters news agency reports, citing sources close to Hamdok.
A protester was shot dead and 125 others were injured during Sunday's mass demonstrations against the October 25 military takeover.
The fight against the coup will continue whether they fire tear gas or bullets, says prominent opposition figure Khalid Omar Youssef.
Civilian groups reject political deal between army chief and prime minister, calling for continuing protests against military rule.
Detained Prime Minister Hamdok was reinstated after agreeing to partner with the military to "stop the bloodshed" but protest organisers have cried "treason".
Sudan's top general, Abdel Fattah al Burhan, and Prime Minister Abdalla Hamdok have signed a political agreement that provides for the premier's reinstatement, release of other civilian leaders and to restore transition to full democracy.
Prime Minister Abdalla Hamdok will lead an independent technocratic cabinet and politicians arrested since the October 25 coup will be released as part of the deal.
Security forces fired live bullets and tear gas after mobile phone communications were cut earlier in the day, witnesses said.
The violence was reported in the capital Khartoum and other cities as thousands of pro-democracy protesters yet again took to the streets across Sudan to rally against the military’s takeover last month.
Abdalla Hamdok has reportedly set the release of all political detainees as a condition for his return to lead the government.
UN head Antonio Guterres says the "reports of violence are alarming and perpetrators must be brought to justice."
At least three protesters have been killed and 80 others wounded, after security forces fired on crowds that flooded the streets in the capital Khartoum in the wake of the ongoing coup in the country.
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