Khartoum's residents said they were shaken awake by warplanes and "violent fighting" between forces loyal to army chief Abdel Fattah al-Burhan and the paramilitary Rapid Support Forces (RSF).
Witnesses told AFP a police base and the state television building in the capital's northwest were under attack by the RSF, who said they had shot down an army MiG fighter.
In central Khartoum, others saw "scores of RSF vehicles" driving towards the vicinity of "the Armoured Corps".
Since April 15, the war between Burhan and his former deputy, RSF commander Mohamed Hamdan Dagalo, has killed nearly 3,000 people and displaced 2.2 million within the country, with another 645,000 fleeing across borders, according to the International Organization for Migration.
"The situation is grave," the medical charity Doctors Without Borders (MSF) said in a statement detailing the hardships of displaced Sudanese stuck in nine camps in White Nile State which borders South Sudan.
In addition to Khartoum, the worst fighting has been in the western region of Darfur where residents, as well as the United Nations, United States and others, say civilians have been targeted and killed for their ethnicity by the RSF and allied Arab militias.
The death toll is believed to be much higher than recorded, as the World Health Organization says about two-thirds of health facilities are "out of service" in combat-affected areas.
Many injured people are unable to reach hospitals, and bodies lie rotting in the streets of Khartoum and Darfur.
A record 25 million people in Sudan need humanitarian aid and protection, the UN says.
According to the MSF, "hundreds of thousands of people, most of them women and children", pack camps that stretch out from the south of Khartoum all the way to the border with South Sudan.
"There are suspected cases of measles, and malnutrition among children has become a vital health emergency. From June 6 to 7 we treated 223 children with suspected measles, 72 were hospitalised and 13 have died," MSF said.
The war has smashed the country's already fragile infrastructure, leaving residents short of water and electricity in the oppressive summer heat.
Numerous ceasefires, including some negotiated by the United States and Saudi Arabia, have failed to hold.
Fighting continued during the just ended Eid al-Adha holiday, for which the warring sides announced separate unilateral truces.
The International Criminal Court charged Bashir and others with genocide, crimes against humanity and war crimes.
A UN official has warned of possible new "crimes against humanity" in the current fighting in Darfur.
Dozens of women have been sexually abused in Darfur and elsewhere, a government unit monitoring such offenses has said.
Most survivors in Khartoum, and "all in Nyala and Geneina" identified the perpetrators as RSF fighters, the unit said.
In early June, Darfur governor and ex-rebel leader Mini Minawi, who is now close to the army, declared Darfur a "disaster zone".
Aid organisations are repeating their appeals to the warring sides to open up secure corridors so they can reach the injured and those displaced by the fighting.
These appeals have taken on increased urgency with the start of the rainy season in Sudan, which is usually accompanied by floods that bring water-borne diseases.