Russia's efforts are aimed at destroying Kharkiv in order to force people to leave the city. Separate rocket and bomb attacks targeted the city's energy infrastructure, The Wall Street Journal noted.
"Putin still wants Kharkiv," said Oleg Synegubov, head of the Kharkiv military administration.
Russia has deployed only a fraction of the forces needed for a possible assault, which estimates could take up to half a million troops.
Oleksandr Lytvynenko, secretary of the National Security and Defense Council of Ukraine, warns that Russia may follow a strategy similar to the one used in 2016 in Aleppo, Syria, when Russian forces destroyed electricity and water supplies, hospitals and schools, displacing a third of the population .
Over the past week, rockets and bombs hit a printing shop and a hypermarket, killing more than 25 people.
City officials are encouraging residents to heed aerial warnings and avoid public places, although evacuations are not considered necessary at this time.