Ukrainian officials said Vladimir Putin’s forces had seized Kreminna, a small town in the Luhansk region.
Moscow has poured troops into the Donbas after last month claiming it would refocus its military efforts on the region. Mr Putin’s forces failed to achieve their key military objective of capturing Kyiv after vastly underestimating the strength of the Ukrainian resistance.
“Kreminna is under the control of the ‘Orcs’ (Russians). They have entered the city," Serhiy Gaidai, the governor of the Luhansk region, told a briefing.
“Our defenders had to withdraw. They have entrenched themselves in new positions and continue to fight the Russian army.”
He said it was “impossible to calculate” the number of civilians killed by Russian forces, adding: “We have official statistics - about 200 dead - but in reality there are many more.”
Elsewhere, the cities of Kharkiv and Kramatorsk came under deadly attack, and Russia also said it struck areas around Zaporizhzhia and Dnipro west of the Donbas with missiles.
Mr Zelensky on Monday warned that the “Battle for the Donbas” had begun as he vowed that his troops would withstand the advance.
“No matter how many Russian troops they send there, we will fight. We will defend ourselves,” he said.
The Pentagon said that it had provided additional military aircraft and parts to repair others in Kyiv’s arsenal that were damaged or inoperable.
"They have received additional aircraft and aircraft parts to help them get more aircraft in the air," Pentagon spokesman John Kirby told a news briefing, adding that Washington had not provided aircraft to Kyiv.
In other developments, a European official told Reuters that the besieged southern city of Mariupol could fall within days as Russia issued an “ultimatum” to Ukrainian soldiers to surrender immediately.
Local authorities say thousands of people have been killed in the siege of the city and Russia has given the last Ukrainian defenders at a steel works an ultimatum to surrender or die.
The city is seen as a strategic asset by the Kremlin as it would help Russia establish a land link between territory it controls in eastern Ukraine and the Crimea region that Moscow annexed in 2014.
Ukraine’s lead negotiator Mykhailo Podolyak said it was difficult to say when ceasefire talks between the two countries would resume as Russia stepped up its attacks in the Donbas and in Mariupol.
"Obviously, against the backdrop of the Mariupol tragedy, the negotiation process has become even more complicated," Mr Podolyak said.
US President Joe Biden consulted with fellow Western leaders "to discuss our continued support for Ukraine and efforts to hold Russia accountable", the White House said.
Prime minister Boris Johnson said that Britain would provide more artillery weapons to Kyiv as the fighting intensified, while German Chancellor Olaf Scholz said Berlin intended to supply Ukraine with anti-tank and air defence weapons.
“This will become an artillery conflict,” Mr Johnson said in parliament.
“They [Ukraine] need support with more artillery, that is what we will be giving them.”