Ukrainian President Volodymyr Zelensky has accused Russia of war crimes after air strikes, including on a central square, in the country’s second city.
At least 10 people were killed and 35 hurt when the opera house, concert hall and government offices were hit in Freedom Square in Kharkiv.
Speaking to the European Parliament, Mr Zelensky urged the EU to prove it was with Ukraine.
Later the main TV tower in the capital Kyiv was hit, putting media off air.
Footage on social media showed smoke billowing from the steel structure.
Five people died in the attack, Ukrainian officials said, but the tower remains standing.
A nearby memorial to victims of the Holocaust was damaged in the same strike. The Babyn Yar ravine is Europe’s largest mass grave of the Holocaust where between 70,000 and 100,000 people, mostly Jews, were shot by the Nazis.
Mr Zelensky said on Twitter that the attack was “history repeating…”.
“What is the point of saying ‘never again’ for 80 years, if the world stays silent when a bomb drops on the same site of Babyn Yar?” he asked.
Meanwhile new satellite images emerged of a huge Russian military convoy which has been outside Kyiv for several days, amid fears of an all-out assault on the capital.
The convoy includes armoured vehicles, tanks, artillery and logistical vehicles, and is said to be less than 18 miles (30km) from the city.
Russia’s defence ministry has urged citizens in militarily sensitive areas of Kyiv to leave their homes.
The ministry, quoted by Tass news agency, said the Russian military was not targeting cities, only military infrastructure, and that there was no threat to the civilian population.
‘Terror against Ukraine’
In a speech for which MEPs gave him a standing ovation, Mr Zelensky thanked the European Union for its support with armaments.
“Without you, Ukraine is going to be alone,” he said. “We have proven our strength.”
“Prove you are with us, prove that you will not let us go.”
Later the Parliament said it would look at a request by Ukraine for candidate status of the EU.
He condemned the attacks on Kharkiv.
“This is the price of freedom,” Mr Zelensky said. “This is terror against Ukraine. There were no military targets in the square – nor are they in those residential districts of Kharkiv which come under rocket artillery fire,” he added.
Video footage showed a missile hitting the local government building and exploding, causing a massive fireball and blowing out windows of surrounding buildings. Freedom Square is the second largest city-centre square in Europe and a landmark of the city.
“Yesterday there was very intense shelling on residential areas,” said Maria Avdeeva, an international security expert currently in Kharkiv.
“Actually, it was the first time that Russia was deliberately targeting houses with people living there,” she told the BBC’s Newsday programme.
“We still have water, it is running in the house. But at any moment Russia could hit the critical infrastructure facilities. There are shortages of food already,” Ms Avdeeva added.
Russia attacks Ukraine: More coverage
Mr Zelensky’s government accuses Russia of trying to lay siege to Kharkiv, Kyiv and other cities.
The sixth day of Russia’s invasion of Ukraine has seen continued attacks on several fronts, but the Russian advance has reportedly been slowed by Ukrainian resistance.
People in the southern city of Kherson say it is now surrounded, and Mariupol, a port city also in the south of Ukraine, is without electricity after an intense bombardment.
Investigation into war crimes
Claims that Russia is committing war crimes are mounting, with growing international calls for the attacks to be investigated.
Russia has previously denied targeting residential areas, but the International Criminal Court (ICC) – which examines war crimes – is looking to open an investigation.
Chief prosecutor Karim Khan still needs the approval of ICC judges to begin work, but for now has asked his team to start collecting evidence of abuses, such as attacks on civilians.
More than 600,000 people across Ukraine have fled their homes to escape the fighting, according to the United Nations, and more than 130 civilians have been killed in Ukraine since Thursday, including 13 children.
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