U.N. special envoy on Sudan Volker Perthes told the U.N. Security Council on Tuesday that the cease-fire "seems to be holding in some parts so far."
But he said that neither party showed readiness to "seriously negotiate, suggesting that both think that securing a military victory over the other is possible."
"This is a miscalculation," Perthes said, adding that Khartoum's airport was operational but the tarmac damaged.
But gunfire and explosions could be heard after nightfall in Omdurman, one of Khartoum's sister cities on the Nile River where the army used drones to target RSF positions, a Reuters reporter said.
The army also used drones to try to drive fighters back from a fuel refinery in Bahri, the third city at the confluence of the Blue Nile and White Nile.
The Sudan Armed Forces (SAF) and paramilitary Rapid Support Forces (RSF) agreed to a 72-hour cease-fire beginning on Tuesday after negotiations mediated by the U.S. and Saudi Arabia.
The fighting has turned residential areas into battlefields. Air strikes and artillery have killed at least 459 people, wounded over 4,000, destroyed hospitals and limited food distribution in a nation where a third of its 46 million people rely on food aid.
"In the capital, Khartoum, 61 percent of health facilities are closed and only 16 percent are operating as normal," WHO chief Tedros Adhanom Ghebreyesus told a press conference from the UN health agency headquarters in Geneva.
The White House said on Wednesday that a second American had died in Sudan on Tuesday amid violence between warring parties.
John Kirby, White House national security spokesperson, told reporters the United States was actively facilitating the departure of a small number of Americans seeking to leave Sudan.
A projectile hit Al-Roumi medical center in Omdurman on Tuesday and exploded inside the facility, injuring 13 people, a hospital official said.
The fighting has paralyzed hospitals and other essential services, and left many people stranded in their homes with dwindling supplies of food and water.
With bodies scattered in the streets, international aid group Medecins sans Frontieres (MSF) said it had been unable to get fresh supplies or personnel into Sudan.
The U.N. humanitarian office (OCHA) said shortages of food, water, medicines and fuel were becoming "extremely acute", prices were surging and it had cut back operations for safety reasons.
The U.N. refugee agency predicted that hundreds of thousands of people might flee into neighboring countries if afforded the opportunity.
A boat with 1,687 civilians from more than 50 countries fleeing violence in Sudan arrived in Saudi Arabia on Wednesday, the foreign ministry said, the largest rescue effort by the Gulf kingdom to date.
The group was "transported by one of the Kingdom's ships, and the Kingdom was keen to provide all the basic needs of foreign nationals in preparation for their departure," the ministry said in a statement.
"I had the chance to leave, not like my sisters," said a tearful Wissam Moustafa, who holds an American passport, as she disembarked a hulking commercial ship that transported more than 1,600 civilians to the coastal Saudi city of Jeddah.
"I don't know whether they will be able to get out."
As foreign governments evacuated their nationals, those with nowhere to go said they felt forsaken.
"Why is the world abandoning us at a time of war?" said Sumaya Yassin, 27, accusing foreign powers of being selfish.
Since the fighting erupted, tens of thousands have left for neighboring Chad, Egypt, Ethiopia and South Sudan.
With civilians leaving Khartoum in cars and buses, the streets of one of Africa's biggest metropolitan areas were largely emptied of ordinary daily life. Those still in the city huddled at home while fighters roamed outside.
“There is nothing left in stores, no water, no food. People have started to go out armed, with axes, with sticks," French journalist Augustine Passilly said by phone as she tried to cross the border into Egypt.
This report was sourced from Reuters and Agence France-Presse.