The army said it was attacking the city to flush out its paramilitary rivals, the Rapid Response Forces (RSF).
The fighting intensified even as the warring sides said they would extend the truce by another three days.
More than 500 deaths have been reported with the true number of casualties believed to be much higher. Millions remain trapped in Khartoum.
Army commander Gen Abdel Fattah al-Burhan and RSF chief Gen Mohamed Hamdan Dagalo, better known as Hemedti, are vying for power – and disagree in particular about plans to include the RSF into the army.
The generals agreed a humanitarian truce after intensive diplomatic efforts by neighbouring countries, the US, UK and UN. It was extended, but did not hold.
However, it remains unclear on what they will do in the next stage of the deal arrived at with US and Saudi mediation, according to the army.