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After a sleepless night as fighting raged, Khartoum residents are cautiously venturing out to buy supplies fearing a prolonged fight between Sudan's regular army and paramilitaries.

"We have been living in terror since yesterday," said 43-year-old Sanaa Mohamed, outside a bakery in a northern Khartoum suburb.

"The explosions terrified my children," added Mohamed, who hurried back to her family immediately after buying bread.

Like many in Sudan, Mohamed was shaken awake on Saturday by the outbreak of deadly fighting between Sudan's army and the powerful paramilitary Rapid Support Forces (RSF).

Families spent the day sheltered in place too scared to move, but on Sunday, with the fighting showing no signs of abating, some have crept out onto the dangerous streets seeking food.

Much of the city is without power in searing temperatures, with people readying for one of the last days of fasting for the holy month of Ramadan.

The violence erupted after weeks of bitter arguments between army chief Abdel Fattah al-Burhan and his deputy, Mohamed Hamdan Daglo, who commands the heavily-armed RSF.

Their disagreements centred around the integration of the RSF into the regular army - a key condition for a final deal aimed at ending a crisis since 2021 military coup that they orchestrated together.

By Saturday morning, the dispute escalated into an all-out conflict with heavy weaponry firing and fighter jets launching airstrikes in Khartoum, and conflict raging in several other cities.

In Khartoum, men in military fatigues on pick-up trucks with mounted machine guns roamed the streets.

Explosions rattled windows - and the nerves of many Sudanese trying to stay safe.

At least 56 civilians have been killed, according to a toll early Sunday by a group of pro-democracy medics, as well as some 600 others wounded.

The two sides have traded blame and accusations over who started the fighting.

Each have claimed the upper hand by declaring control of key sites, including the airport and the presidential palace. None of their claims could be independently verified.

"The shooting never stopped," said Saad Ahmed, 55, from northern Khartoum. At times, "the shelling was as close as 10 metres" from his home, he said.

On social media, Sudanese have shared images of bullet holes in the walls of their homes, warning others to stay away from windows and doors.

The capital has ground to a near halt since the outbreak of clashes, with streets around Khartoum blocked and major bridges sealed off.

Both the army and the RSF have urged people to remain indoors while they fight out their disagreements.

Despite the risk, Farouq Hassan insisted on opening his bakery.

"We are trying to work and make ends meet despite the power and water outages," he told AFP.

Protracted fighting, he fears, would plunge Sudan - already grappling with a spiralling economic crisis - into deeper chaos.

"If I cannot find a way to re-stock the flour, my supply will run out in 48 hours," said Hassan.

The international community and civilian leaders in Sudan have appealed for an immediate ceasefire, but the two generals have yet to heed the calls.

Daglo slammed Burhan as a "criminal" and "liar" on Al Jazeera TV, while the army declared Daglo a "wanted criminal" and the RSF a "rebel militia".

Burhan said there "will be no negotiations or talks until the dissolution" of the group.

"It's very worrying," said Ahmed Seif, who lives in east Khartoum. "It doesn't seem like it will end anytime soon."