A first Red Cross plane laden with humanitarian aid on Sunday landed in Sudan, where deadly clashes between rival generals' forces have entered their third week.

"The eight tonnes of humanitarian cargo includes surgical material to support Sudanese hospitals and volunteers from the Sudan Red Crescent Society," the International Committee of the Red Cross said.

Fighting erupted on April 15 between forces loyal to two rival generals, leaving over 500 people killed and thousands wounded while uprooting tens of thousands more from their homes.

Bodies have remained in the streets in the capital since the conflict began, and the ICRC's Africa regional director, Patrick Youssef, told journalists the Sudanese Red Crescent is "trying to get to the bodies in the streets".

Only 16% of hospitals are functioning in the capital Khartoum, according to the World Health Organization, with many facilities shelled in the fighting.

The shipment took off from the Jordanian capital Amman and arrived in the eastern city of Port Sudan, which Youssef said was now the only entry point for aid to Sudan.

He said the medical kits on the plane were "enough to stabilise 1,500 patients", adding that the ICRC was hoping for security guarantees to send further aid to Khartoum and Darfur.

The regional director said they were able to deliver some aid to Darfur at the beginning, but "it was not enough, and we could not get anything to Khartoum".