The army and the paramilitary Rapid Support Forces (RSF) agreed to extend a week-long ceasefire deal by five days just before it was due to expire late on Monday.
Army leader General Abdel Fattah al-Burhan appeared in a video on Tuesday greeting troops. He said that the army had agreed to the ceasefire extension to ease citizens' access to services.
"The army hasn't used its full deadly power, but it will be forced to do so if the enemy does not obey or listen to the voice of reason," he said in a statement.
"We hope this truce succeeds even if only to stop the war a little and that we can return to our normal lives. We have hope in the truce and we don't have other options," said Hind Saber, a 53-year-old resident of Khartoum.
Hours before the ceasefire extension was signed, residents reported intensive fighting in all three of the adjoining cities that make up Sudan's greater capital around the confluence of the Nile - Khartoum, Omdurman and Bahri.
Residents also reported fighting on Tuesday afternoon near an army base in southern Khartoum.
The United Nations, some aid agencies, embassies and parts of Sudan's central government have moved operations to Port Sudan, in Sudan's Red Sea state, the main shipping hub which has seen little unrest.
On Tuesday, the state's security committee said it had caught several "rebellious" sleeper cells that it said had sneaked in from outside and warned that they were planning activities.
"We thank the citizens of Red Sea state for their total cooperation and for immediately reporting the presence of these rebellious elements and their agents within their neighborhoods," it said, without specifying their identity.
The truce was brokered and is being remotely monitored by Saudi Arabia and the United States, which say it has been violated by both sides but has still allowed for the delivery of aid to an estimated two million people.
The war has caused nearly 1.4 million people to flee their homes, including more than 350,000 that have crossed into neighboring countries.
U.N. children's agency UNICEF said more than 13.6 million children in Sudan, a country of 49 million people, were in urgent need of lifesaving humanitarian support.
The U.N. World Food Program, which expects up to 2.5 million people in Sudan to slip into hunger in coming months, said on Monday that it had begun to distribute food in parts of the capital for the first time since the outbreak of fighting.
The WFP also reported that 17,000 metric tons of food had been looted since the conflict began.