Fighting also took place in El Fasher after Doctors Without Borders gave the army a 48-hour ultimatum to leave its last stronghold in the country.
Sudanese troops and paramilitary Rapid Support Forces (RSF) are fighting near the Gili oil refinery north of the capital Khartoum.
Sudan's army said it had arrived near the strategically important oil refinery on Wednesday after launching a multi-pronged offensive north of Khartoum, amid reports of direct clashes with the Forces Without Borders.
Witnesses said thick smoke filled the sky over large swaths of Khartoum, and videos circulated by Sudanese social media activists showed Sudanese troops controlling the entrance to the town.
"The army has been launching a fierce offensive over the past few days, slowly closing in on the refinery," Al Jazeera's Sheba Morgan reported from Khartoum.
"It's clear that the military is trying to regain control, trying to seize as much territory as possible... but has not yet gained control of the refinery."
Fighting has also been reported in El Fasher, where tensions rose earlier this week when SSF gave Sudanese troops an ultimatum to evacuate the city within 48 hours. After the ultimatum expired, the army carried out airstrikes on MSF positions, according to military sources who spoke to Al Jazeera.
Sources also reported that clashes broke out around the Zarqa complex in northern Khartoum, with heavy weapons used by both sides.
In April 2023, as Sudan descended into conflict, Army Chief of Staff Abdel Fattah al-Burhan and Forces Without Borders leader Mohamed Hamdan “Hemeti” Daga Long-standing tensions have erupted between Mohamed Hamdan “Hemedti” Dagalo and the conflict has displaced some 12 million people.
The war continues to rage, with SSF and the Sudanese army accusing each other of war crimes, including targeting civilians and indiscriminate shelling of residential areas, killing tens of thousands.
More than one million people have fled Sudan's war to neighboring South Sudan, the United Nations refugee agency said on Tuesday. The majority of the millions of people crossing the border are South Sudanese nationals who have previously fled civil war in the world's newest country, the report added.
In another development, South Sudanese authorities suspended access to social media platforms including Facebook and TikTok for at least 30 days following unrest over videos of alleged killings of South Sudanese nationals in Sudan's Gezira state.
At least 16 Sudanese nationals were killed last week after riots broke out across South Sudan, including the capital Juba, in retaliation for the Sudanese military and allied groups' alleged involvement in the Gazira killings.
The head of the National Communications Authority, Napoleon Adoke, wrote to internet service providers on Wednesday, ordering them to cut services before midnight, saying unrest in Sudan "exposes the people of South Sudan to unprecedented levels of extreme violence."