The army official, who spoke on condition of anonymity, said 15 drones targeted Atbara, a city north of the capital, in River Nile province.
He confirmed that strikes caused no casualties.
Local media reports said residents heard explosions.
The official added that ground defences intercepted a smaller-scale drone attack that also targeted Omdruman, the sister city of the capital Khartoum.
The Rapid Support Forces (RSF) drone strikes come a day after the group announced that it agreed to a humanitarian truce proposed by a US-led mediator group known as the Quad.
A Sudanese military official told The Associated Press on Thursday that the army welcomes the Quad's proposal but will only agree to a truce when the RSF completely withdraws from civilian areas and give up weapons per previous peace proposals.
The war between the RSF and the military began in 2023, when tensions erupted between the two former allies that were meant to oversee a democratic transition after a 2019 uprising.
The fighting has killed at least 40,000 people, according to the WHO, and displaced 12 million.
However, aid groups say the true death toll could be many times higher.
More than 24 million people are also facing acute food insecurity, according to the World Food Program.
The US-led plan for a truce would start with a three-month humanitarian truce followed by a nine-month political process, said Massad Boulos, a US adviser for African affairs, earlier this week.
Also Friday, the UN's top human rights body announced it will hold an emergency special session on Sudan on November 14 over recent bloodshed and other violence against civilians in and around the Darfur city of el-Fasher.
The call for the special session by the Human Rights Council in Geneva was led by Britain, Germany, Ireland, the Netherlands and Norway, and has drawn support from two dozen council members in the 47-member-country rights body so far.
The RSF's announcement that it agreed to the truce comes more than a week after the group seized el-Fasher city, which had been under siege for over 18 months.
It was also the last Sudanese military stronghold in Sudan's western Darfur region.
UNICEF said in a Thursday report that more than 81,000 people have been displaced from el-Fasher since October 26, with rising needs for shelter, food, water and medical care, but limited aid delivery.
The UN children's agency said it identified more than 850 children with acute malnutrition who are now receiving treatment.
It added that violence, sexual assaults and looting of health facilities remain rampant across North Darfur, with women and children being the most vulnerable.
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