Ukrainian commanders have predicted that Russia will move troops from Avdiivka to other parts of the front line.
And Ukrainian troops said they were facing “heavy fire” from Russian forces advancing in the southern Zaporizhia region.
Senior commander Oleksandr Tarnavsky said Russia was carrying out a series of attacks near the village of Robotyn – one of the few places where Ukraine regained the lead during a counter-offensive last year.
“These offensive efforts are being stopped, the enemy is being eliminated on the outskirts of Robotin,” Tarnavskiy said in a post on Telegram.
Reports from Russian military bloggers earlier said Moscow’s forces were on the southern edges of the village.
Like many settlements in eastern Ukraine, Robotyn has been completely destroyed by months of artillery fire.
Now towns like Selidov, 30 kilometers (20 miles) from Avdiivka, fear they could be next in line for a Russian invasion. Residents said that an increasing number of Selidov residents are leaving the city.