Russian army commanders told President Vladimir Putin on Friday that Russian troops had taken control of Kostiantynivka although Ukraine denied the claim, saying its forces remained in control of the town.
Kostiantynivka is a key locality whose capture Russia has long sought in its military campaign in the Donetsk region.
Russia said it had proposed a six-hour ceasefire in and around Kostiantynivka on Monday to facilitate the handover of Ukrainian servicemen's bodies and had given Ukraine until Sunday morning to respond.
Ukraine's defence ministry and general staff did not immediately respond to an emailed request for comment.
Ukrainian authorities said on Sunday both Ukraine and Russia again caused a number of casualties and damage on both sides in mutual attacks.
Russia's Gvardeyskoye military airfield on the occupied Crimean Peninsula was attacked during the night, Ukraine's General Staff said on Telegram.
The extent of the damage was initially unclear.
For the Russian military, the airfield is considered the most important base in Crimea.
Ukrainian troops also attacked key transport routes for Russian resupply.
Among other things, two road bridges in the Donbas were destroyed.
The Ukrainian General Staff gave no information about the weapons used.
Russian troops targeted various sites in the eastern Ukrainian city of Kharkiv in the afternoon.
At least one person was killed and 11 others injured in attacks using drones and missiles, Kharkiv governor Oleh Syniehubov said on Telegram.
with DPA
