Each side appears to be battling for control of territory in the capital ahead of any possible negotiations, though the leaders of both factions have shown little public willingness to hold talks after more than two weeks of fighting.
"Since yesterday evening, and this morning, there are air strikes and the sounds of clashes," said Al-Sadiq Ahmed, a 49-year-old engineer speaking from Khartoum.
"We've got into a state of permanent terror because the battles are around the centers of residential neighborhoods. We don't know when this nightmare and the fear will end."
Heavy bombardments also rang out in the adjoining cities of Omdurman and Bahri. Both sides had agreed to a seven-day ceasefire, which has been violated.
The army said it killed RSF fighters and destroyed a number of vehicles "belonging to the rebels," after clashing with the group in the Bahri military region.
The RSF accused the army of breaching a ceasefire and attacking forces since dawn. It said the army attacked its residential neighborhoods with artillery and aircraft in a "cowardly manner."
U.S. President Joe Biden on Thursday said weeks of urban fighting in Sudan "must end" and authorized potential new sanctions against those responsible for the bloodshed.
"The violence taking place in Sudan is a tragedy - and it is a betrayal of the Sudanese people's clear demand for civilian government and a transition to democracy," he said in a statement. "It must end."
Clashes between rival factions began on April 15 and have killed an estimated 700 people, mostly in Khartoum and Darfur, according to the Armed Conflict Location and Event Data Project.
The United Nations, meanwhile, pressed Sudan's warring factions on Wednesday to guarantee safe passage of humanitarian aid after six trucks were looted and air strikes in the capital undermined a supposed truce.
U.N. aid chief Martin Griffiths said he hoped to have face-to-face meetings with Sudan's warring parties within two to three days to secure guarantees from them for aid convoys to deliver relief supplies.
The United Nations has warned that fighting between the army and RSF, which erupted on April 15, risks causing a humanitarian catastrophe that could spill into other countries. Sudan said on Tuesday that 550 people had died and 4,926 people wounded so far in the conflict.
About 100,000 people have fled Sudan with little food or water to neighboring countries, the U.N. says.
While wealthy countries like the United States and Britain sent planes to evacuate their nationals from an airfield near Khartoum, many Africans and other foreigners from less resourced countries struggled to find a way out.
Thousands piled into buses and trucks for the 800 km journey by road from Khartoum to Port Sudan on the Red Sea to board ships. Others headed 1,000 km north to Egypt's frontier, only to get stuck in days-long queues to be allowed to cross.
Nigeria's National Emergency Management Agency said Egypt was only allowing its nationals to enter if they had places on a flight out. A Nigerian air force plane and a charter flight evacuated the first 354 Nigerians from the Egyptian city of Aswan on Wednesday.
Egypt's Foreign Ministry did not immediately respond to a request for comment. It has said authorities were providing relief and emergency services at the crossings and trying to speed up entry procedures by reinforcing border staff.
