A man walks by a house hit in recent fighting in Khartoum, Sudan on Tuesday. Marwan Ali/Associated Press

CAIRO — Sudanese and foreigners streamed out of the capital of Khartoum and other battle zones, as fighting Tuesday shook a new three-day truce brokered by the United States and Saudi Arabia. Aid agencies raised increasing alarm over the crumbling humanitarian situation in a country reliant on outside help.

A series of short cease-fires the past week have either failed outright or brought only intermittent lulls in the fighting that has raged between forces loyal to the country’s two top generals since April 15. The lulls have been enough for dramatic evacuations of hundreds of foreigners by air and land, which continued Tuesday.

But they have brought no relief to millions of Sudanese caught in the crossfire, struggling to find food, shelter and medical care as explosions, gunfire and looters wreck their neighborhoods. In a country where a third of the population of 46 million already needed humanitarian assistance, multiple aid agencies have had to suspend operations and dozens of hospitals have been forced to shut down. The U.N. refugee agency said it was gearing up for potentially tens of thousands of people fleeing into neighboring countries.

Calls for negotiations to end the crisis in Africa’s third-largest nation have been ignored. For many Sudanese, the departure of diplomats, aid workers and other foreigners and the closure of embassies are terrifying signs that international powers expect the mayhem to only worsen.

U.N. Secretary-General Antonio Guterres warned that the power struggle between rival generals and their military forces is not only putting Sudan’s future at risk, “it is lighting a fuse that could detonate across borders, causing immense suffering for years, and setting development back by decades.”

The U.N. chief urged the Sudanese military, commanded by Gen. Abdel Fattah Burhan, and the rival Rapid Support Forces, a paramilitary group led by Gen. Mohammed Hamdan Dagalo, “to silence the guns” immediately.

“The conflict will not, and must not, be resolved on the battlefield,” Guterres told an emergency meeting of the U.N. Security Council late Tuesday.

U.N. special envoy for Sudan Volker Perthes, who moved from Khartoum to Port Sudan with most U.N. staff and many humanitarian organizations, accused both warring parties of fighting “with disregard for the laws and norms of war,” citing attacks on densely populated areas.

With supply lines running out, he said, there is mounting fear of increased criminality, and “reports of prisoners being released from detention centers across Khartoum have compounded these fears.”

Smoke is seen in Khartoum, Sudan on Saturday. The fighting in the capital between the Sudanese Army and Rapid Support Forces resumed after an internationally brokered cease-fire failed. Marwan Ali/Associated Press

Thousands of Sudanese have been fleeing Khartoum and its neighboring city of Omdurman. Bus stations in the capital were packed Tuesday morning with people who had spent the night there in hopes of getting on a departing bus.

Drivers increased prices, sometimes tenfold, for routes to the border crossing with Egypt or the eastern Red Sea city of Port Sudan. Fuel prices have skyrocketed, to $67 a gallon from $4.20, and prices for food and water have doubled in many cases, the Norwegian Refugee Council said.

Those lucky enough to reach the border crossings face additional hardships.

Moaz al-Ser, a teacher, arrived at the Arqin border crossing with Egypt early Tuesday with his wife and three children after a harrowing trip from Omdurman. They were among hundreds of families who were waiting to be processed. Many had spent the night in an open area near the border.

“The crossing point is overwhelmed and authorities on both sides don’t have the capacity to handle such a growing number of arrivals,” he said.

Secretary-General Guterres cited reports of armed clashes across the country, with people fleeing their homes in Blue Nile and North Kordofan states and across Western Darfur as well. Terrified people remain trapped indoors with dwindling food, water, medicine and fuel, and health services near collapse, he said.

Jordanians evacuated from Sudan arrive at a military airport in Amman, Jordan on Monday. Raad Adayleh/Associated Press

Joyce Msuya, the assistant secretary-general for humanitarian affairs, said at least 20 hospitals have been forced to close due to damage, military use or lack of resources. She also told the council “there have been numerous reports of sexual and gender-based violence.”

The 72-hour cease-fire announced by U.S. Secretary of State Antony Blinken was to last until late Thursday night, extending a nominal three-day truce over the weekend.

The rival forces said Tuesday they would observe the cease-fire. In separate announcements, they said Saudi Arabia played a role in the negotiations.

But fighting continued, with explosions, gunfire and the roar of warplanes overhead around the capital region.

“They stop only when they run out of ammunition,” Omdurman resident Amin Ishaq said. Al-Roumy, a medical facility in Omdurman, said it suspended its services after it was hit by a shell Tuesday.

“They don’t respect cease-fires,” said Atiya Abdalla Atiya, a senior figure in the Sudan Doctors’ Syndicate, a group that monitors casualties.

Dr. Bushra Ibnauf Sulieman, a Sudanese-American physician who headed the Faculty of Medicine at the University of Khartoum, was stabbed to death outside his home, the Doctors’ Syndicate said. He had practiced medicine for many years in the United States, where his children reside, but had returned to Sudan to train doctors. Colleagues said he had been treating those wounded in the fighting in recent days and that it was not known who killed him.

The World Heath Organization, meanwhile, expressed concern that one of the warring parties had seized control of the central public health laboratory in Khartoum.

“That is extremely, extremely dangerous because we have polio isolates in the lab. We have measles isolates in the lab. We have cholera isolates in the lab,” Dr. Nima Saeed Abid, the WHO representative in Sudan, told a U.N. briefing in Geneva by video call from Port Sudan.

He did not identify which side held the facility but said they had expelled technicians and power was cut, so it was not possible to properly manage the biological materials. “There is a huge biological risk.”

Clashes meanwhile escalated in the western Darfur region, residents said. Armed groups, wearing RSF uniforms, attacked several areas in Genena, a provincial capital, burning and looting properties and camps for displaced people.

“Fierce battles are raging all over the city,” said a doctor in Genena, who asked to remain anonymous for fear of reprisals. “All eyes are on Khartoum but the situation here is unimaginable.”

Women and children were fleeing homes in the city center, and the city’s main hospital has not functioned for days, with unknown numbers of dead and wounded, she said.

More fighters on motorcycles and horses have flowed into the city to join the battles, with dead bodies lying in the streets, according to Darfur 24, an online news outlet focusing on covering the war-wrecked region.

The RSF has its roots in Darfur, where it emerged from the notorious Janjaweed militias that committed atrocities there while putting down a rebellion in the 2000s.

At least 459 people, including civilians and fighters, have been killed, and over 4,000 wounded since fighting began, the U.N. health agency said, citing Sudan’s Health Ministry. Among them were 166 deaths and over 2,300 wounded in Khartoum, it said.

Secretary-General Guterres said four U.N. staff were killed. The U.N. said they were three Sudanese working for the World Food Program and one Sudanese working for the International Organization for Migration.

Those who are able have made their way to the Egyptian border, Port Sudan or relatively calmer provinces along the Nile. But the full scale of displacement has been difficult to measure.

Msuya said the U.N. has received reports “of tens of thousands of people arriving in the Central African Republic, Chad, Egypt, Ethiopia, and South Sudan.”

Mohammed Mahdi, of the International Rescue Committee, warned that resources were growing thin at the Tunaydbah refugee camp in eastern Sudan after 3,000 people fleeing Khartoum took refuge there, joining some 28,000 refugees from Ethiopia.

At least 20,000 people have fled from Khartoum to the city of Wad Madani 100 miles to the south, the U.N. Office for the Coordination of Humanitarian Affairs said. Some 20,000 Sudanese have fled to Chad and around 4,000 South Sudanese refugees living in Sudan have returned home, according to the U.N. refugee agency, which is gearing up for tens of thousands more to flee to neighboring countries.

Associated Press writers Jill Lawless in London, Kirsten Grieshaber in Berlin, and Edith M. Lederer at the United Nations, contributed to this report.