With the battle for control of Sudan entering its third week, health care services are rapidly unraveling in the nation’s capital, Khartoum, a grim consequence of the brutal fighting that has raised fears the conflict could devolve into a wider humanitarian crisis.

The total collapse of the health care system could be days away, the Sudan Doctors’ Trade Union warned.

Hospitals have been shelled, and two-thirds of those in Khartoum have closed, according to the World Health Organization. More than a dozen health care workers have been killed, officials say. Beyond that, “hidden victims” are dying of illness and disease as basic medical services have become scarce, said Dr. Abdullah Atia, secretary general of the doctors’ union.

“We receive a lot of calls every day: ‘Where shall I go?’” he said. “These are the questions we are not able to answer.”

Millions of civilians remained trapped. The latest truce to allow civilians to escape was to end at midnight on Sunday, and though the Rapid Support Forces said it would extend a humanitarian cease-fire for three more days, fighting was reported in the capital.

The Sudanese Army agreed in a statement on Sunday to extend the truce, but it has accused the Rapid Support Forces of violating the truce and of occupying a hospital. The R.S.F., in turn, has said the army has been looting medical supplies.

In response to the worsening situation, the United Nations secretary general’s office said it was “immediately” sending Martin Griffiths, the under secretary general for humanitarian affairs and emergency relief coordinator, to Sudan.

“The scale and speed of what is unfolding is unprecedented in Sudan,” Stéphane Dujarric, spokesman for the secretary general, said in a statement.

Other nations have scrambled to evacuate their citizens by any means necessary as the situation has deteriorated. Britain had airlifted more than 2,122 people by Saturday on 21 flights, with one more flight from Port Sudan in eastern Sudan planned for Monday, the British government announced on Sunday. Americans have fled in long convoys of buses, trucks and cars heading to Egypt to the north or to Port Sudan, where they hope to board ships to Jeddah, Saudi Arabia.

The State Department said on Sunday that a second convoy of U.S. citizens had arrived in Port Sudan, bringing the number of evacuated Americans to just under 1,000. The department added that fewer than 5,000 Sudanese citizens had sought the U.S. government’s help via a “crisis intake” website set up for Americans and their families. About 16,000 Americans live in Sudan, many of them dual citizens.

Sudan’s Health Ministry is nowhere to be found, with the doctors’ union saying it had received no support and little communication from the government. Health facilities have been used by fighters as defensive positions, witnesses and officials say.

What’s more, the paramilitary forces have occupied the national laboratory, officials say. Samples of diseases like malaria or tuberculosis could become weaponized in the wrong hands, said Dr. Atia, who, like others, spoke by phone from Khartoum.

Uncollected bodies in morgues and others in the street are another concern, he added. The doctors’ union later said in a statement that the number of bodies scattered on the streets was growing, creating “an environmental catastrophe.”

Hundreds of doctors have fled, and there are rumors that fighters with the Rapid Support Forces are kidnapping medics and forcing them at gunpoint to treat their wounded comrades. While the abductions have not been confirmed, Dr. Atia said, dozens of members of the Sudan Doctors’ Trade Union are unaccounted for.

The shortage of health care workers has left hospitals with barely enough staff to cope. Al Ban Jadid hospital in east Khartoum usually has a staff of at least 400 people but now has only eight health care workers. Al Joda Hospital in southern Khartoum is hobbling along with four people: a surgeon, an anesthetist and two nurses, Dr. Atia said.

“Health care workers in Sudan have been doing the impossible, caring for the wounded without water, electricity and basic medical supplies,” Patrick Youssef, the Red Cross’s regional director for Africa, said in a statement.

The Sudan doctors’ union issues a notice on Facebook several times a day listing the few hospitals still operating in Khartoum, or an urgent alert for doctors to report to the field hospitals set up in homes across the city.

Away from hospitals, medical staff must use whatever tools they can find to treat the wounded.

In a field hospital in Al Mamoura, Dr. Mohamed Karrar improvised an intercostal drain system using a sterilized soda bottle to pump the blood from a gunshot victim’s punctured lung. Long shifts in the trauma ward of the now-shuttered Ibrahim Malik Teaching Hospital in central Khartoum helped prepare him, but Dr. Karrar must now contend with the sound of war while working in a living room converted into an operating room.

“I know I’m in danger in these areas,” he said, “but those sick, wounded people need me.”

At Al Nada, medical workers and their patients take cover multiple times a day under beds and tables, hiding from aerial bombardments and heavy artillery fire. Everyone is so jittery, said a doctor there, Mohamed Fath, that the sound of an oxygen canister being opened can send staff fleeing.

Early in the conflict, the management at Al Nada, a private facility, decided to treat only pregnant women and children in order to provide a haven for a small fraction of the more than 24,000 women who, according to the W.H.O., are expected to give birth in Sudan in the next few weeks.

In the weeks since the fighting began, 220 babies have been born there, and most have survived, Dr. Fath said.

One woman sped through active combat zones and barely made it to the emergency room, he said. Later, her husband showed Dr. Fath the bullet holes in his car. Another woman gave birth at home, but because of complications the baby needed urgent medical care. The mother and child were trapped in their home for days with artillery fire whizzing overhead, the doctor said. When they finally made it to the hospital, it was too late for the infant, who died.

“They have to go through this hell to get to the hospital,” Dr. Fath said.

Neighbors seeking care have taken to ringing Dr. Fath’s doorbell at home. Twice last week, he said, he pronounced two people dead in Omdurman Althawra, north of the city. Both were diabetics who ran out of insulin in a city where pharmacies have been ransacked and a medical black market is thriving.

Now, the doctor said, he spirits home medicine hidden in his car. But in neighborhoods that can quickly turn from ghost towns to active war zones, even the mile-long trip between the hospital and his home can imperil his life.

Before the war, Dr. Fath was filling out application forms to work in hospitals in South Africa, where he planned to specialize in pediatric neurology. But he and his wife, also a doctor, whose final exam was set for May 6, made the decision to stay.

“If you see what I saw every day, in a day-to-day practice,” Dr. Fath said, “you would understand my situation.”

Edward Wong contributed reporting from Washington, Nailah Morgan from New York and Isabella Kwai from London.