At least 528 people have been killed and almost 4,600 people wounded in the violence, according to Sudan's health ministry, but the death toll is feared to be far higher.
Battles erupted on April 15 between Sudan's de facto leader Abdel Fattah al-Burhan, who leads the regular army, and his ex-deputy Mohamed Hamdan Dagalo, who commands the powerful paramilitary Rapid Support Forces.
Millions of Sudanese around the capital have since hidden in their homes with dwindling food, water, and electricity as warplanes on bombing raids have drawn heavy fire from anti-aircraft guns.
"Warplanes are flying over southern Khartoum and anti-aircraft guns are firing at it," said one resident, while another witness told AFP he was also hearing "loud gunfire" in the area.
Fighting has also spread across Sudan, especially in the long-troubled Darfur region, where witnesses reported intense conflict and looting.
At least 96 people were reported killed in El Geneina, West Darfur, the UN said.'
As of Monday, at least 20,000 people had found refuge at a makeshift camp in the Chadian border village of Koufroun, according to the United Nations refugee agency UNCHR, which manages their influx along with other UN agencies.
The village lies a few hundred meters from the border with West Darfur, which with the capital Khartoum is among the worst-hit provinces in the Sudan conflict.
Most of those arriving have come from the Sudanese town of Tendelti, about 20 kilometers away.
UN Secretary-General Antonio Guterres said he was "immediately" sending Martin Griffiths, his emergency relief coordinator, to the area "in light of the rapidly deteriorating humanitarian crisis in Sudan."
"The scale and speed of what is unfolding is unprecedented in Sudan. We are extremely concerned by the immediate as well as long-term impact on all people in Sudan, and the broader region," Stephane Dujarric, the spokesperson for Guterres, said in a statement.
Sudan's already troubled health sector faces the risk of "disaster" after more than two weeks of heavy fighting have rocked the poverty-stricken country, a UN World Health Organization official warns.
Even before the deadly conflict broke out on April 15, "the healthcare system in Sudan faced numerous crises... and was extremely fragile," Ahmed al-Mandhari, WHO regional director for the eastern Mediterranean, told AFP.
Now - with hospitals bombed, medicines running low and many doctors fleeing the country - "it is a disaster in every sense of the word," he said, warning of the growing threat of cholera, malaria and other diseases.
Burhan and Dagalo have agreed multiple, poorly observed ceasefires, and extended the latest formal truce on Sunday by 72 hours, with each side repeatedly blaming the other for the frequent violations.
Top UN humanitarian official Martin Griffiths said Sunday he was heading to the region to help "bring immediate relief to the millions of people whose lives have turned upside down overnight".
"The humanitarian situation is reaching breaking point," he said. "Goods essential for people's survival are becoming scarce in the hardest-hit urban centers, especially Khartoum."
"The cost of transportation out of worst-hit areas has risen exponentially, leaving the most vulnerable unable to locate to safer areas."
Some 50,000 people have fled the raging conflict, seeking refuge in neighboring countries including Chad, Egypt, and the Central African Republic, said the UN refugee agency.
The fighting has also triggered a mass exodus of foreigners and international staff, with countries the world over launching frantic evacuations by land, sea, and air.
Further complicating the battlefield, Central Reserve Police were being deployed across Khartoum to "protect citizens' properties" from looting, the Sudanese police said, confirming an army statement.
The RSF had warned police against joining the fight.
The UN World Food Program has warned the unrest could plunge millions more into hunger in a country where 15 million people already needed aid to stave off famine.
Only 16 percent of health facilities are functioning in Khartoum, according to the World Health Organization, with many facilities shelled.
On Sunday, a first Red Cross plane brought eight tons of humanitarian aid from Jordan to Port Sudan, which is so far untouched by the fighting and has served as an evacuation hub.
The aid included surgical material and medical kits to stabilize 1,500 patients.
Regional powers have joined negotiations to help end the violence.
An envoy of Burhan's met on Sunday in Riyadh with the Saudi Arabian Foreign Minister Prince Faisal bin Farhan, who called for the restoration of calm in Sudan, his ministry said.
Egypt called an Arab League meeting of its permanent delegates Monday to discuss the "situation in Sudan."