Residents dodged gunfire in the capital, Khartoum, as rival forces battled over the presidential palace, state TV, and army headquarters.
Twenty-five people, including 17 civilians, have died in the city, a doctors' organization said.
The clashes erupted after tensions over a proposed transition to civilian rule.
Both the army and its opponents, the Rapid Support Forces (RSF), claimed they had control of the airport and other key sites in Khartoum, where fighting continued overnight.
Heavy artillery was heard in Omdurman, which adjoins Khartoum, and nearby Bahri in the early hours of Sunday morning. Eyewitnesses also reported gunfire in the Red Sea city of Port Sudan.
The army said jets were hitting RSF bases, and the country's air force told people to remain in their homes on Saturday night while it conducted a full aerial survey of paramilitary activity.
Residents of Khartoum told the foreign media of their panic and fear, with one describing bullets being fired at the house next door.
At least 56 civilians have been killed in cities and regions around the country, a Sudanese doctors' committee said, adding that dozens of military personnel were dead, some of whom had been treated in hospitals.
In total, at least 595 people had been injured, it said.
Three employees for the World Food Programme (WFP), a UN body that delivers food assistance to vulnerable communities, were killed after the RSF and armed forces exchanged fire at a military base in Kabkabiya, in the west of the country.
Generals have been running Sudan since a coup in October 2021.
The fighting is between army units loyal to the de facto leader, Gen Abdel Fattah al-Burhan, and the RSF, commanded by Sudan's deputy leader, Mohamed Hamdan Dagalo, also known as Hemedti.
Hemedti said his troops would keep fighting until all army bases were captured.