Sudan's army chief Gen Abdel Fattah Al Burhan pledged on Tuesday to fight the Rapid Support Forces to the last soldier, amid heavy fighting in Khartoum at the start of a new, five-day truce mediated by the US and Saudi Arabia.
The truce went into effect on Monday night on the expiry of an earlier, seven-day ceasefire that brought a lull in the fighting to the capital.
But it did not allow much humanitarian relief to reach the millions trapped in the city with dwindling food supplies, and near-total water and power shortages.
The US and Saudi Arabia remotely monitor compliance with the ceasefire.
Gen Al Burhan, speaking to soldiers at the Khartoum headquarters of an army unit called the Strategic Brigade, said his soldiers were fighting the paramilitary RSF on behalf of every Sudanese citizen.
"We are not fighting with our maximum firepower but we will if the enemy does not succumb," he said.
"We will continue to fight until the last soldier standing is killed.
Gen Al Burhan was wearing green-and-black camouflage fatigues with its sleeves rolled up, and an AK-47 slung over one shoulder.
The Strategic Brigade, in Khartoum's Mugrin district near the confluence of the White and Blue Niles, came under heavy attack by the RSF soon after footage of Gen Al Burhan speaking there surfaced online, residents said.
The paramilitary force said its troops were attacked the Strategic Brigade but they repelled them, chased them back to their base and seized it.
The RSF claim could not be independently verified.
There was also fighting on Tuesday night in Bahri and Omdurman, Khartoum's two adjoining sister cities across the Nile.
Residents said there had been air strikes by the army, artillery shelling and heavy gunfire.
Footage of thick black smoke billowing from a building surfaced online with a voiceover saying the structure belonged to the UN Children's agency, Unicef.
The RSF said that an army air strike destroyed the offices of a UN agency, but gave no further details.
Since it started on April 15, the war in Sudan has killed hundreds of people and injured thousands.
The UN says more than a million people have been internally displaced and nearly 350,000 have fled abroad, including more than 170,000 to Egypt.
Those still in Khartoum have been hiding from street fighting and roaming looters in the city of nearly seven million, of whom nearly 700,000 have fled, according to the UN.
More than six weeks into the conflict, more than half the population – 25 million people – are in need of aid and protection, the UN says.
Among them are 13.6 million children, including 620,000 suffering from severe malnutrition, "half of whom may die if not helped in time", Unicef said.
On Sunday the UN said 53 lorries with life-saving supplies – about a third of those planned – had been able to reach their destinations since the seven-day truce began.
The fighting sparked mass evacuations of thousands of foreign nationals in the initial weeks, while many abandoned foreign embassies and consulates were ransacked.
Libya on Tuesday denounced "the assault and looting" of its Khartoum embassy.
The fighting has also spilt over into Darfur, the vast western region already ravaged by two decades of war and civil strife.
Activists and aid workers say Darfur civilians continue to be attacked, entire districts have been burnt to the ground and tens of thousands of people have been forced to flee into Chad.
The UN has warned for weeks that fighting in Darfur's major cities between the army and the RSF has also drawn in local militias, tribal fighters and armed civilians.
Darfur's pro-army Governor, Minni Minawi, a former rebel leader, has urged citizens to "take up arms" to defend their property, a move that threatens to turn the fighting there into a full-fledged civil war.
With additional reporting by AFP