Ukraine's General Staff said on Facebook fighting had intensified particularly around the strategic city of Pokrovsk in the Donetsk region, where Ukrainian forces said they repelled 70 attacks over the course of Sunday, with 12 more ongoing.
The town serves as a key transport hub and Russian forces are reportedly approaching from the east, south and southwest.
The information could initially not be independently verified.
Attempts by Russia to break through to the west into the neighbouring industrial area of Dnipropetrovsk have so far been repelled by Ukraine.
Meanwhile, Russia's air defence systems destroyed 26 Ukrainian drones overnight, TASS news agency reported on Monday citing Russia's defence ministry data.
The attacks come despite ongoing diplomatic efforts by the United States to broker a ceasefire between Moscow and Kiev.
US President Donald Trump recently proposed an unconditional 30-day truce, a plan Ukrainian President Volodymyr Zelenskiy accepted.
However, Russian President Vladimir Putin rejected the offer.
Instead, Putin has declared a unilateral 72-hour ceasefire to coincide with the annual Victory Parade on Moscow's Red Square to mark the end of World War II, which is celebrated in Russia on Friday.
The ceasefire is scheduled to start at midnight Wednesday-Thursday in Moscow and end at midnight Saturday-Sunday.
Kiev has rejected the limited pause and demanded that the ceasefire be extended to 30 days.
"The Russians are asking for a ceasefire on May 9 and are themselves firing at Ukraine every day. This is cynicism of the highest order," Zelenskiy wrote on Telegram on Sunday.
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