Kharkiv has come under sustained shelling from Russian forces since the outbreak of the war.
The heavy bombardment has destroyed buildings, killed hundreds of people and forced thousands more to flee their homes.
Russian troops have repeatedly tried to take control of Ukraine’s second largest city, but have so far failed.
They attempted to storm the city last night from Piatykhatky, a suburb nine miles to the north, Oleh Sinehubov, the regional administrator for the area announced on Telegram.
He said Kharkiv’s defenders were able ‘to push the enemy back beyond its previous position,’ in what he described as a ‘shameful defeat’ for Russia.
The assault came after Russian forces firing more than 60 missiles on Monday, according to local reports.
Shells hit the city’s historical centre, including its main marketplace with rescuers seen pulling the bodies of dead civilians from destroyed apartment buildings.
At least 500 people in Kharkiv have been killed since the outbreak of war on February 24.
The constant pounding from Russia means many who stayed are now forced underground, either to escape the shells or because their homes were destroyed.
In the Saltivka neighbourhood, people have moved into the basement of a school a few metres from where their homes once stood.
Pictures show people trying to keep themselves busy in the dark conditions surrounded by what belongings they could bring with them.
Elsewhere in the district, former shelters have been abandoned as more buildings are damaged by Russian shells.
Dr Pavel Nartov, the director of the Kharkiv Regional Clinical Infectious Diseases Hospital, said air raid sirens go off multiple times a day, forcing fragile patients into the hospital’s makeshift bomb shelter.
The hospital has been treating people with Covid-19 throughout the pandemic and has a number of virus patients on its wards.
Dr Nartov said moving ICU patients on ventilators is dangerous but also crucial, given the risks of exposing oxygen tanks to bombings or flying shrapnel.
‘Bombing takes place from morning into night. Thank God a bomb has not yet hit our hospital. But it could hit at any time,’ he told The Associated Press.
Elsewhere in the city photos have shown empty and partially destroyed supermarkets as people struggle to find enough food and water to survive.
Russia-Ukraine war: Everything you need to know
Over 3 million people have fled, as Ukrainian cities face shortages of food, water, heat, and medicine – with thousands of British people opening up their homes to Ukrainian refugees.
Countries have retaliated by imposing sanctions on Russia and oligarchs such as Roman Abramovich, while large companies like Disney, Starbucks, McDonald’s, and Coca-Cola have suspended business in the country.
However, despite these economic blows, Russian President Vladimir Putin hasn’t shown any signs of calling off the attack anytime soon.
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