The army has used airpower against RSF units dug into residential areas of Khartoum.
Aid supplies that have arrived in Port Sudan for other aid agencies still awaiting safe passage to Khartoum,
Foreign countries have carried out their own evacuation effort.
Over 100,000 refugees are estimated to be among people who have fled Sudan to neighbouring countries, including Sudanese refugees, South Sudanese returning home prematurely and others who were themselves refugees in Sudan, UN officials said on Tuesday as gunfire and explosions echoed across the capital despite another ceasefire deal.
The conflict risks morphing into a broader disaster as Sudan's impoverished neighbours deal with a refugee crunch and fighting hampers aid deliveries in a nation where two-thirds of people already rely on some outside assistance.
Egyptian President Abdel-Fattah al-Sisi said Cairo would provide support for dialogue in Sudan between the rival military factions but was also being careful about not interfering in their domestic matters.
"The entire region could be affected," he warned in an interview with a Japanese newspaper on Tuesday as an envoy from Sudan's army chief, who leads one of the warring sides, met Egyptian officials in Cairo.
United Nations officials had said UN aid chief Martin Griffiths aimed to visit Sudan on Tuesday, but the timing was still to be confirmed.
The UN's World Food Programme said on Monday it was resuming work in the safer parts of the country after a pause earlier in the conflict, in which some WFP staff were killed.
"The risk is that this is not just going to be a Sudan crisis, it's going to be a regional crisis," said WFP's East Africa Director Michael Dunford.
No sign of backing down
The commanders of the army and paramilitary Rapid Support Forces (RSF) who previously shared power as part of an internationally backed transition towards free elections and civilian government show no sign of backing down, yet neither seem able to secure a quick victory. That has raised the spectre of a prolonged conflict that could draw in outside powers.
Early on Tuesday, black smoke could be seen hanging over the capital Khartoum, which lies at the confluence of the Blue and White Nile rivers. “Air strikes hit Bahri on the east bank, while clashes flared in Omdurman to the west,” witnesses said.
Hundreds of people have died in the fighting that pits the army under General Abdel-Fattah al-Burhan against the RSF under General Mohamed Hamdan Dagalo, also known as Hemedti. Each has blamed the other for the violation of a series of ceasefires.
The army has used airpower against RSF units dug into residential areas of Khartoum, damaging swathes of the capital area and reigniting conflict in Sudan's far west Darfur region.
“Port Sudan where thousands of people have fled Khartoum seeking evacuation abroad, is the main entry point for aid for many countries in the region,” the WFP's Dunford told Reuters.
"Unless we stop the fighting, unless we stop now, the impact on a humanitarian scale is going to be massive," he said.
“Kenya has offered the use of its airports and airstrips near the border with South Sudan as part of an international humanitarian effort,” Kenyan Foreign Minister Alfred Mutua said.
Aid supplies that have arrived in Port Sudan for other aid agencies were still awaiting safe passage to Khartoum, a road journey of about 800 km, although Medecins Sans Frontieres (MSF) said it had delivered some aid to Khartoum.
“Some 330,000 Sudanese have also been displaced inside Sudan's borders by the war,” the UN migration agency said.
Thousands of Sudanese are trying to exit the country, many across the borders with Egypt, Chad and South Sudan. The UN warned on Monday that 800,000 people could eventually leave including refugees living in Sudan temporarily.
At the border with Egypt, where more than 40,000 people have crossed over the past two weeks, delays are causing refugees to wait for days before being let through after paying hundreds of dollars to make the journey north from Khartoum.
Foreign countries have carried out their own evacuation effort, with an airlift from outside the capital and long road convoys to Port Sudan where ships have ferried them abroad.
Most European countries have ended their evacuation efforts. Russia said on Tuesday it had pulled out 200 of its citizens.
The army and RSF had shared power since a 2021 coup but had fallen out over the timeline for a transition to civilian rule and moves to merge the RSF into the regular military.
The two had fought side by side to battle an uprising in Darfur from 2003 onwards in which more than 300,000 people died, raising accusations of genocide.