The source of the gunfire was not immediately known.
The rift between the forces came to the surface on Thursday, when the army said that recent movements by the Rapid Support Forces (RSF), a powerful paramilitary group, had happened without coordination and were illegal.
On Friday and early on Saturday, the heads of both the army and RSF told mediators that they were ready to take steps to de-escalate the situation.
A confrontation between them could spell prolonged strife across a vast country already dealing with economic breakdown and flare-ups of tribal violence.