Severodonetsk, the largest city under Ukrainian control in Luhansk province, has come under intense artillery and missile fire from Moscow’s forces.
On Sunday, local officials said Russian troops were repelled after trying to enter the city from four directions.
It comes as Ukraine’s President Volodymyr Zelensky urged world leaders to end all trade with Russia.
Speaking via video link at the annual World Economic Forum in Davos, Mr Zelensky called for “maximum sanctions” to be imposed on Moscow, saying frozen Russian funds should be used to rebuild Ukrainian cities destroyed by the war.
“There has to be a precedent for punishing the aggressor,” Mr Zelensky said. “If the aggressor loses everything then it definitely deprives him of any motivation to start a war.”
Meanwhile, Luhansk Governor Serhiy Gaidai accused Moscow of adopting a “scorched-earth approach” in its efforts to capture the city of Severodonetsk.
“Every day they are trying to break the line of defence,” Mr Gaidai said. “They are simply systematically destroying the city. Everywhere is being shelled constantly.”
The city of 100,000 people sits on a strategic position on the Donets River, with UK defence officials saying it has likely become one of Russia’s “immediate tactical priorities”.
Mr Gaidai warned that Russian forces have destroyed all but one bridge across the Donets river and said that the city is at risk of being cut off.
He also accused Russian tanks of firing on residential buildings during fighting in the city and of seeking to erase Severodonetsk “from the face of the earth”.
Ukraine’s human right’s ombudsman, Lyudmyla Denisova, said the city risks suffering the same fate as Mariupol – being surrounded and pounded into submission.
“The enemy threw all his forces to storm Severodonetsk, on the outskirts of which there are constant battles,” Ms Denisova wrote on Telegram.