NAIROBI, Kenya — As a new wave of violence swept the Sudanese capital, Khartoum, on Monday, millions of residents hiding in their homes felt the growing strain from the battles, and doctors and hospitals were struggling to cope with casualties and get the supplies and staff members that they needed.

The forces of rival generals battling for control of Sudan clashed for a third day in Khartoum, threatening to worsen a humanitarian crisis in a nation already facing dire economic straits, growing hunger and widespread unemployment.

The fighting has left many of Khartoum’s five million residents stranded at home without electricity or water as they marked the last few days of Ramadan, the Muslim holy month when many fast daily from dawn until dusk. Some were too afraid to venture out for food or other supplies.

A doctors’ group said that hospitals remained understaffed and were running low on supplies as wounded people streamed in. And the World Health Organization said that the insecurity in the capital was impeding medical workers and ambulances from reaching those in need of critical care.

The fighting, which erupted on Saturday, has pitted a paramilitary group known as the Rapid Support Forces against the Sudanese Army — a longstanding rivalry between Sudan’s two top generals who have been vying for dominance over the northeast African nation. It was still not clear who was in control of the country even as both sides claimed crucial victories.

The death toll from the first two days of fighting rose to 97, according to the Central Committee of Sudanese Doctors.

Khartoum residents said there was an escalation in the number of fighter jets and helicopters that were circling the city starting at about 3 a.m. local time Monday. Two people in an area close to the city’s international airport said the planes were circling every few minutes and getting very close to their homes.

“It’s like they are on top of our heads,” said Dallia Mohamed Abdelmoniem, a resident who was taking shelter with 10 people, including family members.

In the Kafouri suburb north of Khartoum, one resident said the jets had hit a camp belonging to the Rapid Support Forces. Two major explosions also rocked the neighborhood, shattering windows and leaving the homes in the area shaking. It was not immediately clear if those blasts resulted in casualties.

There was intense street fighting and blasts in several neighborhoods, including in the upscale Riyadh neighborhood and the Burri suburb, residents said.

The Central Committee of Sudanese Doctors said that 41 people, a majority of them in Khartoum, were killed in clashes on Sunday, bringing the toll for the first two days of fighting to 97. There was no immediate word on casualties from Monday’s fighting. Nearly 350 people were injured, according to the committee.

For decades, Sudan has suffered under the yoke of dictatorship, coups and political instability, with successive governments overseeing widespread repression and genocidal violence, particularly in the Darfur region. The country has struggled to shake off its troubled history even after the longtime autocrat Omar Hassan al-Bashir was ousted in 2019.

Over the past few years, generals have steadily tightened their grip on the nation, killing and jailing civilians and repeatedly scuttling any attempt to transition to democratic rule. The tension between the army chief, Gen. Abdel Fattah al-Burhan, and the head of the paramilitary Rapid Support Forces, Lt. Gen. Mohamed Hamdan, had been simmering for months now and finally ruptured into violent confrontations between their forces on Saturday morning.

The conflict has further dimmed Sudan’s hope of moving toward democracy.

The clashes across Sudan have drawn worldwide concern, with regional and global leaders along with humanitarian and aid organizations calling on both parties to cease the violence.

The Intergovernmental Authority on Development, an eight-nation regional bloc that Sudan belongs to, said on Sunday that it would dispatch the presidents of Kenya, Djibouti and South Sudan to mediate between the parties.

On Monday, U.S. Secretary of State Antony J. Blinken said there was a “shared deep concern” among the United States and its allies over the fighting in Sudan, and called for the violence to end immediately. Mr. Blinken also urged the two generals to “ensure the protection of civilians and noncombatants as well as people from third countries” who are currently in Sudan.

Edward Wong contributed reporting from Karuizawa, Japan.