The sound of artillery fire shook the dawn in northwest Khartoum and progressed towards the centre and east of the city on Monday, witnesses told AFP.
The fighting "began at 0200 GMT and is still going," one resident said.
The war-torn capital barely saw a few hours of respite after heavy clashes on Sunday between troops loyal to army chief Abdel Fattah al-Burhan and those of the paramilitary Rapid Support Forces (RSF) led by Gen. Mohammad Dagalo.
Later on Monday, witnesses reported the air force targeted an armoured RSF convoy as it wound its way from the country's south towards Khartoum.
War-weary civilians have largely rejected Gen. al-Burhan's call for army volunteers, instead pleading for an end to the relentless war between al-Burhan and his former deputy, Rapid Support Forces commander Mohamed Hamdan Dagalo.
Apart from Khartoum, some of the worst fighting has been in the vast western region of Darfur, where late on Sunday RSF forces "attacked the military base" in Nyala, the capital of South Darfur.
Darfur is home to a quarter of Sudan's population and is still scarred by a two-decade war. Residents there 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 RSF has been accused of intentionally targeting civilians in Darfur, including by shooting people fleeing towards the Chadian border.
The paramilitaries have also been identified as the main perpetrators of conflict-related sexual assault by survivors in both Darfur and Khartoum.
According to the governmental Combating Violence Against Women and Children Unit, most of the 42 survivors in Khartoum - and all of the 46 survivors in the Darfur cities of Nyala and El Geneina - said they were assaulted by RSF fighters.
Late on Sunday, the RSF announced it was cracking down on "looting and vandalism, particularly the theft of civilian cars."
Since the conflict began, RSF fighters - highly mobile and embedded in densely populated neighbourhoods - have been accused of widespread break-ins and looting.
Residents have been forcibly evicted from their homes, had their vehicles stolen, or learned after fleeing Khartoum that their homes were being used as bases.
The RSF announced last week it had begun to try some of its "undisciplined" members.