A videograb show a huge fire at the Greater Nile Petroleum Oil Company Tower in Khartoum on Sunday. AFP

"Clashes are now happening around the army headquarters with various types of weapons," one Khartoum resident, who declined to be named, told reporters.

Other witnesses in southern Khartoum said they heard "huge bangs" as the army targeted bases of the Rapid Support Forces paramilitaries with artillery.

Witnesses also reported fighting in the city of El Obeid, 350 kilometres south.

Nawal Mohammed, 44, said battles Saturday and Sunday between the regular army and the paramilitaries have been "the most violent since the war began".

Though her family lives at least three kilometres away from the nearest clashes, Mohammed said "doors and windows shook" with the force of explosions, while several buildings in central Khartoum were set alight.

In social media posts users shared footage of flames devouring landmarks of the Khartoum skyline, including the ministry of justice and the Greater Nile Petroleum Oil Company Tower -- a conical building with glass facades that had become an emblem of the city.

Other posts showed buildings -- their windows blown out and their walls charred or pockmarked with bullets -- smouldering.

"It's distressing to see these institutions destroyed like this," Badr Al Din Babiker, a resident of the capital's east, told reporters.

Since war erupted on April 15 between army chief Abdel Fattah Al Burhan and his former deputy, RSF commander Mohamed Hamdan Daglo, nearly 7,500 people have been killed, according to a conservative estimate from the Armed Conflict Location & Event Data Project.

Civilians and aid workers have warned that the real toll is far higher, as many of those injured or killed never make it to hospitals or morgues.

A committee of volunteer pro-democracy lawyers on Sunday said the fighting in Khartoum since Friday had killed dozens of civilians in "continued disregard for international humanitarian law."

"We are working to determine the number of civilian victims" of "arbitrary shelling," the group said in a statement.

The war in Sudan has decimated already fragile infrastructure, shuttered 80 percent of the country's hospitals and plunged millions into acute hunger.

More than five million people have been displaced, including 2.8 million who have fled the relentless air strikes, artillery fire and street battles in Khartoum's densely-populated neighbourhoods.

Millions who could not or refused to leave Khartoum remain in the city, where water, food and electricity are rationed.

The violence has also spread to the western region of Darfur, where ethnically-motivated attacks by the RSF and allied militias have triggered renewed investigations by the International Criminal Court into possible war crimes.

There has also been fighting in the southern Kordofan region, where witnesses again reported on Sunday artillery fire exchanged between the army and the RSF in the city of El Obeid.

Agence France-Presse