According to the UN, since fierce combat started out between opposing groups on April 15, more than 100,000 people have fled Sudan.
If the conflict does not stop, officials have issued a "full-blown catastrophe" warning.
Within Sudan, an additional 334,000 people have been displaced.
Despite a ceasefire that is supposed to be in effect, fighting between the army and the paramilitary Rapid Support Forces (RSF) is still taking place in the capital, Khartoum.
Volker Perthes, the UN's special representative for Sudan, told the AP news agency on Monday that the two sides have agreed to begin negotiations for a "stable and reliable" ceasefire.
The negotiations may take place in Saudi Arabia, he suggested.
If negotiations are successful, it will be the first time the two sides have met since the war began.
According to Sudan's health ministry, more than 500 people have died and more than 4,000 have been injured in the conflict.
Following several brief cease-fires that didn't last, the military kept bombarding Khartoum with airstrikes in an effort to weaken the RSF.
Fighting has also been intense in western Sudan's Darfur region.
Olga Sarrado, a spokeswoman for the UN agency for refugees, told journalists in Geneva that the number of 100,000 includes persons from Sudan, South Sudanese nationals going back home, and those who were already refugees within Sudan escaping the conflict.
Additionally, refugees have been crossing the border between Sudan and Chad and Egypt in the north.
The majority of European nations have finished evacuating their citizens, but on Tuesday, Russia said that it was sending four military aircraft to transport out more than 200 individuals from Sudan, including its citizens and those from "friendly countries."
Food, water, and power are in short supply in Khartoum, but because of the unrest, much-needed assistance supplies that were transported by the UN to Port Sudan are being stored. There is currently no secure method of delivering them due to rampant looting.
Ahmed al-Mandhari, regional director for the World Health Organisation (WHO), claimed that Khartoum's health institutions have been attacked and some are being utilised as military camps.
"Up to now, there were around 26 reported attacks on healthcare facilities. Some of these attacks resulted in the death of healthcare workers and civilians in these hospitals," he told the BBC.
"Also you know some of these hospitals are used as military bases and they have thrown the staff, they have thrown patients out of these healthcare facilities," he added.
Abdou Dieng, the UN's human resources coordinator in Sudan, said on Monday that the country's ongoing humanitarian crisis ran the risk of becoming a "full-blown catastrophe" after more than two weeks of bloody combat.
"Nearly 16 million people, or one-third of Sudan's population, need humanitarian help even before the present crisis. According to him, 3.7 million people had already been internally displaced, primarily in Darfur.