Eight Ukrainian troops have been killed and 26 wounded since fighting intensified on Sunday - the heaviest losses for the military since mid-December, according to government figures.
"The current escalation in Donbass is a clear indication of Russia's continued blatant disregard of its commitments under the Minsk agreements with a view of preventing the stabilization of the situation and achieving any progress in the security and humanitarian spheres," Ukraine's foreign ministry said in a statement.
The peace deal was agreed in February 2015, but international security monitors report ceasefire violations on a daily basis, including regular gun and mortar fire.
The latest clashes mark the first significant escalation in Ukraine since the inauguration of U.S. President Donald Trump, whose call for better relations with Moscow has alarmed Kiev while the conflict remains unresolved.
Ukrainian authorities said they were prepared for a possible evacuation of Avdiyivka's 16,000 residents, many of whom have little or no access to electricity or water after shelling from the separatist side hit supply infrastructure.