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Russia has struck an apartment block in the north-east Ukrainian city of Kharkiv, killing at least three people and injuring 31 more, say local officials.

The wave of strikes, which officials said had hit four districts, was conducted with the use of guided glide bombs on Tuesday.

"The targets for Russian bombs are a residential building, a bakery, a stadium... that is, the ordinary life of ordinary people," said Ukraine's President Volodymyr Zelensky.

The attack comes as fighting intensifies in the country's east with Russian troops encircling and closing in on the largely destroyed town of Vuhledar.

Shortly after Tuesday's blitz in Kharkiv, Zelensky issued a statement sharing pictures of the destroyed residential tower - which showed a gaping hole in the middle of the building.

He called on allies to "stop the terror". He is in New York to address the UN General Assembly's annual congress, having arrived on Monday reiterating Ukraine's need for timely US military assistance.

"There is much discussion now at the UN General Assembly about collective efforts for security and the future. But we just need to stop the terror. To have security. To have a future," Zelensky said.

Meanwhile in Kharkiv, officials said the block that was hit had previously been struck at the start of the war.

"It was almost repaired, all the windows were put in, insulated, and prepared for the heating season. The enemy hit it a second time with a KAB [glide bomb]," said Kharkiv's mayor Ihor Terekov on Telegram.

Russia has increasingly been using glide bombs in recent months - Soviet-era bombs fitted out with wings and satellite navigation aids. They are cheap, destructive, and are said to have been key to Russia's effort to capture further ground in Ukraine.

They were used in May in attacks in Kharkiv, while military analysts also note that they appear to have been on Sunday night.

Ukrainian officials said Russia conducted seven airstrikes with KAB glide bombs, injuring at least 21 civilians in the attacks on 13 residential buildings and two educational facilities.

Zaporizhzhia officials also said Russia had conducted another strike on the south-eastern city on Monday night, which killed one person and injured at least four others including two children.

Russian forces have made serious advances in Ukraine's east and are closing in on Vuhledar - a coal-mining town on the southern part of the Donbas front line. The Russians have been trying to seize the town since the beginning of their full-scale invasion.

On Monday, Russian military bloggers were reporting that Moscow's troops had entered the outskirts of the town in the Donetsk region. Ukraine's military has mentioned only a number of attempts to capture its positions in Vuhledar.

Meanwhile, Russian forces have also recently advanced near Hlyboke, Kupyansk, and Pokrovsk, according to the US-based think tank the Institute for the Study of War.

The war tracking group said Ukrainian forces had recently advanced in Kursk region.