But Kyiv says Moscow has massed troops around Avdiivka and sent in heavy equipment, enabling it to hit back hard.
It says Moscow aims to encircle and capture the town, just northwest of the Russian-occupied city of Donetsk, and draw in Ukrainian troops from other fronts.
Russia's Defence Ministry said on Thursday its forces had inflicted damage on Ukrainian troops in areas including Avdiivka but gave few details.
It estimated that Russian forces have captured 4.52 square kilometres (1.75 square miles) of territory around Avdiivka since the beginning of their offensive on Tuesday.
Geolocated footage indicated that Russian forces had likely lost at least a battalion tactical group's worth of armoured vehicles in the Avdiivka offensive, it said.
Persons:
Alexander Ermochenko, Avdiivka, Barabash, Andriy Yermak, Anna Pruchnicka, Timothy Heritage, Robert Birsel
Organizations:
REUTERS, Russian, Reuters, Russia's Defence, General, of Ukraine's Armed Forces, Thomson
Locations:
Avdiivka, Russia, Ukraine, Donetsk, Russian, Ukrainian, Moscow, Crimea, American