Ukraine authorities have said at least 10 people were killed and 35 injured in attack on the city of Kharkiv.
Ukrainian officials say Russia has targeted a TV tower in Kyiv, hitting nearby broadcast facilities.
It comes after Russia warned residents that it was preparing to hit targets in the Ukrainian capital.
Russia said it was planning attacks on Kyiv technology centres and urged people to stay away.
A huge convoy of Russian armoured vehicles continues to advance on the city.
Earlier, Russian missiles and rockets hit the cultural heart of Ukraine's second largest city in what officials said was a deadly and "cruel" attack.
An opera house, concert hall and government offices were hit in Freedom Square, in the centre of the north-eastern city Kharkiv.
Local authorities have said at least 10 people were killed and 35 injured.
Indian medical student killed
India's foreign ministry has confirmed that a medical student was killed on Tuesday in shelling in Kharkiv after he left the bunker he had been sheltering in to buy food.
One of his friends said the 22-year-old student had spoken to him shortly before his death.
He was in his fourth year at Kharkiv National Medical University.
Thousands of Indian citizens are still in Ukraine and are pleading to be evacuated after Russian troops invaded.
India has launched an operation to get its citizens home but has been facing logistical hurdles.
Walk out
On Tuesday, representatives from Europe and other allies walked out during a video link address by Russia's Foreign Minister Sergey Lavrov at the UN Conference on Disarmament in Geneva.
A video posted by the French delegation showed dozens of officials leaving the chamber while Mr. Lavrov started his address via video link.
During his speech to the UN Human Rights Council, Mr. Lavrov said he did not attend in person because of what he called outrageous measures by European Union in applying sanctions on Russia following its unprovoked invasion of Ukraine.
At the same meeting, Ukraine's foreign minister accused Russia of war crimes through its shelling of his country and called for a special meeting to address Russian aggression and weapons of mass destruction.
A minute of silence was held for the victims of fighting in Ukraine.
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