A least four people have died after an airstrike hit a building sheltering civilians in the city of Lysychansk on Thursday.
A further seven people were wounded, Luhansk regional governor Serhiy Haidai said.
“The rescue operation is still going,” he wrote on Telegram following airstrike in Ukraine’s embattled eastern city.
Mr Haidai added that a separate airstrike earlier on Thursday had struck a sanatorium building in Lysychansk, causing it to collapse.
He anticipated the possibility of further further casualties.
“It is likely that there are people trapped under the rubble,” he said of the second strike.
A second rescue effort is underway there.
Lysychansk is close to the city of Severodonetsk, which has been subjected to weeks of intense Russian bombardment.
The two cities are the only remaining ones to have not been captured by Russia in the eastern region of Luhansk.
On Wednesday, the United Nations said that thousands of civilians are trapped in Severodonetsk with a diminishing supply of clean water, sanitation and electricity.
An urgent situation is developing at the Azot chemical plant in the city, where it is believed hundreds of people are seeking refuge in makeshift bunkers beneath the plant.
A spokesperson for UN Humanitarian Affairs office, Saviano Abreu, told the BBC that the embattled city is running out of basic services.
Severodonetsk, a key manufacturing centre and has been under intense bombardment for the past few weeks as the fight for control of the Donbas intensifies.
Earlier this week, Volodymyr Zelensky said Ukrainian forces were experiencing painful losses in fighting in eastern Ukraine.
He also described the battle for Severodonetsk as “terrifying”, adding that the human cost of the battle was “very high”.
