Saudi Arabia and the United States, which brokered a week-long cease-fire deal and have been monitoring it remotely, announced shortly before it was due to expire on Monday evening that the parties had agreed to extend it.
Although the cease-fire had been imperfectly observed, it had allowed the delivery of aid to an estimated two million people, the two countries said in a joint statement.
"The extension will provide time for further humanitarian assistance, restoration of essential services, and discussion of a potential longer-term extension," the statement said.
Sources with knowledge of the new deal said discussions on amendments to make the truce more effective were continuing.
Hours earlier, residents reported battles in all three of the adjoining cities that make up Sudan's greater capital around the confluence of the Nile - Khartoum, Omdurman and Bahri. The intensity of the fighting was greater than over the past three days, they said.
Sudan's army and the paramilitary Rapid Support Forces (RSF) have been locked in a power struggle that erupted into conflict on April 15, killing hundreds and driving nearly 1.4 million people from their homes.
Air strikes, which the army has been using to target RSF forces embedded in neighborhoods across the capital, could be heard in Omdurman on Monday afternoon, residents said.
"Since yesterday evening there has been bombardment with all types of weapons between the army and the Rapid Support," Hassan Othman, a 55-year-old resident of Omdurman, told Reuters by phone. "We're in a state of great fear. Where's the truce?"
On past days, the truce deal had brought some respite from heavy fighting, though sporadic clashes and air strikes have continued.
Saudi Arabia and the U.S. have previously said both sides had committed various violations of the truce, as well as impeding humanitarian access and restoration of essential services.