Prime Minister Abdalla Hamdok announced his resignation in a speech on Sunday.
The news comes almost three months after the military coup in Sudan where he was ousted - only to sign an agreement with the military a month later and return to his post but with a government ruled by the military.
On Sunday, Hamdok announced that he had resigned in a political stalemate.
Two killed in protests
Since the military coup, thousands of Sudanese have protested against the military junta and several have been killed.
On Sunday, two people were shot dead during a demonstration in the town of Omdurman.
One of the dead was shot in the chest while the other suffered severe head injuries, according to the Medical Committee, which is part of the pro-democracy movement.
During a demonstration with 1,000 participants outside the presidential palace in the capital Khartum, security forces used tear gas, reports an AFP journalist on the spot.
The protesters shouted "power to the people" and demanded a transition to a civilian government in the country.
Limited internet and telephone use
Prior to the demonstration, the security forces had set up roadblocks in the capital and severely limited the possibility of using the internet and telephone.
The street protests against General Abdel Fattah al-Burhan's coup have been going on for over two months.
The protests have been repeatedly met with violent opposition from the security forces.
56 people have been killed in clashes
On Thursday, five people were shot dead in Khartoum when security forces clashed with large demonstrations.
At least 56 people have been killed in clashes between security forces and protesters during protests that have been going on since the military coup in October, according to the Medical Committee.