Ukrainian soldiers are withdrawing from positions in the shattered town of Avdiivka after advancing Russian forces breached a critical supply line and threatened to encircle scores of Ukrainian soldiers, Ukrainian military officials and soldiers said on Thursday.

Dmytro Lykhovii, a spokesman for Ukrainian forces fighting in the area, said the Ukrainians were “maneuvering” and “sometimes withdrawing to more advantageous positions and sometimes repelling enemy advances.”

He also said military commanders had set up a backup logistical route to the town to transport much needed supplies to Ukraine’s beleaguered troops.

The battle, Mr. Lykhovii said, was dynamic and changing by the hour as the two sides engaged in fierce urban combat. But his comments suggested the fighting had taken another ominous turn for Kyiv’s forces, potentially presaging their withdrawal from a town reduced to ruins by months of horrendous bombardment.

In a war of mostly small territorial gains, the capture of Avdiivka would be the Russians’ most significant battlefield achievement since taking Bakhmut last May.