As the war in Sudan heads into its fourth month, Omdurman — the city across the Nile River from the capital, Khartoum — has become the site of some of the most fierce fighting between the two forces battling for power: the army and its rival, the paramilitary Rapid Support Forces.

Patients were admitted in droves in recent days to one of the few functioning health facilities left in Omdurman, their bodies riddled with bullets or sliced by shrapnel from airstrikes. Some victims were dead by the time they were brought in, their passage hindered by street battles in Omdurman, once a bustling business hub and home to many universities, hospitals and political and cultural institutions.

“It’s been like hell,” said Dr. Rashid Mukhtar Hassan, the human resource manager at the health facility, Al-Nau Teaching Hospital, in a phone call.

The Rapid Support Forces have extended their hold on the capital, according to residents, military analysts and humanitarian officials in touch with those stuck in the war zone. The clashes have intensified as the army has tried to block the paramilitary group’s supply routes coming from its stronghold in Darfur, in western Sudan.

The fighting continued on Monday even as a major international meeting to broker a cease-fire began in the Ethiopian capital, Addis Ababa. Sudan’s army boycotted the talks, insisting that the chairman — President William Ruto of Kenya — was not neutral. Egypt also plans to hold a summit on July 13 to find ways to end the conflict.

In a sign of the global concern about the war, the talks included leaders and officials from nearby African countries, the United Nations, Saudi Arabia and the United States, including Molly Phee, the U.S. assistant secretary of state for African affairs.

The war in the northeastern African nation, which erupted on April 15, has led to a devastating humanitarian crisis and fears of destabilization in the already fragile Horn of Africa region.

More than 3,000 people have been killed and 6,000 others injured, according to Sudan’s minister of health, though aid workers say the toll is most likely higher. Medical workers, humanitarian staff and refugees have been targeted in the violence. At least 22 people were killed in an airstrike this past weekend.

Dr. Hassan said that his hospital had received 125 injured civilians and 20 bodies in the course of one day last week. Three more died during surgery. Afterward, he said, he used his car to deliver some of the deceased to their families.

“It was the worst day ever,” said Dr. Hassan, 42, who was reached in two phone calls in recent days.

The conflict has displaced more than 2.2 million people inside the country, with about 700,000 others crossing to neighboring countries including Chad, Egypt and South Sudan, according to the International Organization for Migration.

Sexual violence has also been pervasive, according to the United Nations, with girls as young as 12 being assaulted, according to the aid group Save the Children.

From the onset, the paramilitary forces had a greater presence than the army on the ground in Khartoum and the adjoining cities of Omdurman and Bahri. They also captured the Yarmouk ammunitions factory in June, seized areas east of the strategic Halfaya Bridge and recently took over the south Khartoum and Omdurman Central Reserve Police bases, according to residents and analysts.

“The Rapid Support Forces delivered a strong initial sucker punch to the army,” said Alan Boswell, the Horn of Africa project director at the International Crisis Group.

But as the war grinds on, he said, the Rapid Support Forces have been trying to bring more troops and equipment into the capital from their stronghold in Darfur, especially as the rainy season gets underway.

“We are entering a new phase of the conflict where this is now becoming a war over supply lines,” Mr. Boswell said. “And Omdurman is at the heart of it.”

The army has sought to undermine those operations, conducting ground offensives and intense air raids on paramilitary strongholds, including near the state broadcasting compound in Omdurman.

The army has also tightened its presence near strategic posts it already controls, including the Wadi Saeedna air base just outside Khartoum and the General Command headquarters.

Outside the capital area, the army remains dominant across northern and eastern Sudan. However, the paramilitary forces have also tightened their command over Darfur, a region blighted by decades of genocidal violence. The outbreak of war has brought renewed, vicious ethnic violence to parts of Darfur.

In recent weeks, the Rapid Support Forces have conquered Zalingei, the capital of Central Darfur, and have secured victories against the army in Nyala, the capital of South Darfur, according to residents, analysts and United Nations officials. In West Darfur, the army’s troops rarely left their bases as violence tore through cities like El Geneina, said residents and aid workers who fled the city. The paramilitary forces have also besieged El Obeid, the capital of North Kordofan, where there are two sites of strategic value: an airport and an oil refinery.

Humanitarian aid workers say they have faced bureaucratic hurdles to release shipments or attain visas. Much of the international aid is being coordinated through the army-controlled coastal city of Port Sudan, which is over 1,000 miles from some of the worst-affected parts of the country, like West Darfur.

William Carter, the country director for the Norwegian Refugee Council, who has been coordinating aid deliveries from Kosti, a town about four hours south of Khartoum, said there was an urgent need to establish more humanitarian corridors to deliver aid quickly.

“Every day that passes adds to the unbearable catastrophe that civilians across the country must face pretty much on their own,” he said.

But with the diplomatic talks deadlocked and both sides calling for fresh mobilization, worries persist about a protracted conflict.

“We are exhausted and working in a difficult situation,” said Dr. Hassan, just after he took medication to treat his malaria.

“I am shivering but we cannot just quit helping Sudanese people,” he said.