"Five members of the convoy were killed and several more people were injured. Multiple trucks were burned, and critical humanitarian supplies were damaged," the UN children's agency and the World Food Programme said in a joint statement.
They did not say who was responsible and called for an urgent investigation into the attack, which they said was a violation of international humanitarian law.
Without fresh supplies soon, hundreds of thousands of people in al-Fashir are at "high risk of malnutrition and starvation," the UN joint statement said.
Aid has frequently come under crossfire in the two-year-old war between the Sudanese army and the paramilitary Rapid Support Forces, which has left more than half the population facing crisis levels of hunger and driven millions from their homes.
In statements, the RSF and the army blamed each other for the latest attack.
The RSF said the army had attacked in an air strike, while the army said the RSF had torched the truck.
Reuters could not independently verify the contradictory accounts.
The UN joint statement said the route of the 15-truck convoy, which travelled more than 1800km from Port Sudan, had been shared with the parties in advance.
It was negotiating access to complete the journey when it was attacked, it said.
Al Koma is controlled by the RSF, and earlier this week was the scene of a drone strike that claimed several civilian lives, according to local activists.
Famine conditions have previously been reported in al-Fashir, the capital of North Darfur.
The fighting and barriers to the delivery of aid put in place by both sides have cut off supplies.
The attack is the latest of several assaults on aid in recent days.
It follows the repeated shelling of UN World Food Programme premises in al-Fashir by the RSF and an attack on El Obeid hospital in North Kordofan that killed several medics late last month.
