DONETSK, Ukraine — The Ukrainian military on Sunday moved into the heart of the separatist hub of Luhansk for the first time, officials said, chipping at one of the cornerstones of the pro-Russia rebels’ disintegrating virtual state.

Ukrainian officials said army units had raised the national flag over a police station in central Luhansk, the eastern city that, along with Donetsk, has been a center of rebel activity and an important destination for Russian fighters and aid. Other parts of Luhansk, however, were still said to be under rebel control.

The claim could not be independently confirmed, though a photograph of the flag and police station was circulating on social media, and the report was consistent with the progress of fighting there going into the weekend.

Along with increased Ukrainian pressure on rebel positions in Donetsk, the army’s move into Luhansk focused attention on the profound reversal of the separatists’ fortunes since they declared independence in April. Interviews across eastern Ukraine portray a rapid breakdown in discipline in the rebel ranks. Many fighters have abandoned their uniforms in favor of civilian clothes, and three senior leaders have left the war zone in recent days.