Sudan's army has denied backing Tigray fighters and instead says the rival RSF paramilitary is receiving support from within Ethiopia, according to Al Jazeera.
Authorities have not released casualty or damage figures for the blaze at the Umm Alila facility.
The Sudan Doctors Network said the Sodari Rural Hospital had served more than 50,000 families before the war.
The defecting commander says the decision followed tragedies he witnessed within the paramilitary group.
Sudan's army says it has seized the strategic North Kordofan city of Sodiri, claiming heavy losses for the paramilitary Rapid Support Forces, which has yet to respond to the claim.
The Sudan Doctors Network said the strikes hit neighborhoods in El-Obeid, capital of North Kordofan state, from dawn through midday, according to Anadolu Agency.
The governor of Bau said government troops pushed back RSF and allied fighters from two areas, according to Anadolu Agency.
Military sources tell Anadolu Agency that Sudanese forces seized the al-Jamama area after clashes with the paramilitary Rapid Support Forces.
Sudan's military says it killed RSF fighters and destroyed nine vehicles in a preemptive attack south of Al-Keili.
Military sources cited by Anadolu Agency say government forces seized several locations after clashes with the Rapid Support Forces.
A drone attack attributed to Sudan's Rapid Support Forces on a court in North Kordofan state killed at least 13 people, according to Al Jazeera.
According to RFI, there has been no contact with the journalist since he left his media outlet, Saraounia radio and television, in Niamey on the evening of August 31.