The fighting has continued despite the U.S.-brokered ceasefire that took effect on Tuesday, with warplanes patrolling the skies over the capital's northern suburbs as fighters on the ground have exchanged artillery and heavy machine gun fire, witnesses said.
Late Wednesday, the army said it had agreed to talks in Juba, capital of neighboring South Sudan, on extending the three-day truce which expires on Friday "at the initiative of IGAD," the East African regional bloc.
The RSF's response to the proposal remains unclear.
There have been multiple truce efforts since fighting broke out on April 15 between Sudan's regular army led by General Abdel Fattah al-Burhan and the paramilitary Rapid Support Forces (RSF) commanded by his deputy turned rival, Mohamed Hamdan Dagalo. All have failed.
U.S. Secretary of State Antony Blinken said Thursday that the United States was working with Sudan's warring generals to extend an expiring, shaky ceasefire that he helped broker.
Blinken said he expected to say more "in the coming hours" on the situation in Sudan, where the army has renewed air strikes on rival paramilitaries in the capital Khartoum even before the truce expires at midnight (2200 GMT).
"We are very actively working to extend the ceasefire," Blinken told reporters.
"We've had a 72-hour ceasefire, which like most ceasefires is imperfect but nonetheless has reduced violence. And that's obviously created somewhat better conditions for people in Sudan," he said.
Blinken said that the United States was also working to establish a more regular route for the departure of foreigners from Sudan.
At least 512 people have been killed and 4,193 wounded in the fighting, according to health ministry figures, although the real death toll is likely to be much higher.
The doctors' union said at least eight civilians had been killed in Khartoum alone on Wednesday despite the truce.
More than two thirds of hospitals in the country were out of service, the union said Thursday, including 14 that had been struck during the fighting.
Beyond the capital, fighting has flared in the provinces, particularly in the war-torn western region of Darfur.
Clashes between the army and the RSF raged for a second straight day in the West Darfur capital Geneina, witnesses said, adding that civilians were seen fleeing to the nearby border with Chad.
"We are locked up at home and too afraid to go out so we can't assess the scale of the damage," said a resident who asked to remain anonymous for his safety.
"The heavy fighting began from 24 April," he said, confirming severe damage to hospitals and public buildings and looting across the city.
On Wednesday, the United Nations humanitarian agency had reported killings, looting and arson in Geneina.
"An estimated 50,000 acutely malnourished children have had nutrition support disrupted due to the fighting," it added in a statement.
The heavy fighting has trapped many civilians in their homes, where they have endured severe shortages of food, water and electricity. Communications have been sporadically disrupted.
The U.N. has warned that as many as 270,000 people could flee into Sudan's poorer neighbors South Sudan and Chad.
Other Sudanese have sought refuge in Egypt to the north and Ethiopia to the east, but both entail long and potentially dangerous journeys overland.
The U.N. said it had "received reports of tens of thousands of people arriving in the Central African Republic, Chad, Egypt, Ethiopia, and South Sudan."
Cambridge University academic Sharath Srinivasan warned that the mass movement of people across Sudan's borders threatened to destabilise already fragile regimes in neighbouring countries.
"If the armed confrontation between these two forces protracts - or worse, if it draws in other armed rebel groups across the country - this could quickly become one of the worst humanitarian crises in the region and risk spilling over," he told U.S. news outlet Politico.
Foreign governments have taken advantage of the fragile truce to organize road convoys, aircraft and ships to get thousands of their citizens out but some have warned their evacuation efforts are dependent on the lull in fighting holding.
A Saudi evacuation ship docked in the Red Sea port of Jeddah Thursday carrying 187 Sudan evacuees from 25 countries, including the United States, Russia and Turkey, the Saudi foreign ministry said.
It was the eighth such crossing organized by the Saudi authorities since the start of the fighting and took the total evacuated to the kingdom so far to 2,544, only 119 of them Saudis, the ministry said.