Russian missiles and rockets have 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.

At least 10 people were killed and 35 more were injured, local authorities have said.

The attack came as Ukraine's president said Russia was committing war crimes.

"This is the price of freedom," President Volodymyr 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.

Kharkiv has been bombed heavily for days now, and 16 people were killed before Tuesday's attack Mr Zelensky said. His government accuses Russia of trying to lay siege to Kharkiv and other cities, including the capital Kyiv, where a huge Russian armoured convoy is approaching.

Ukraine's Foreign Minister Dmytro Kuleba said the world must do more to punish Russia for the "barbaric" attack on Freedom Square and residential neighbourhoods, accusing the Russian President Vladimir Putin of committing "more war crimes out of fury, murdering innocent civilians".

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 the mayor of Mariupol, a port city also in the south of Ukraine says it endured relentless shelling overnight.

Meanwhile new satellite images showed a 40-mile (64km) long Russian military convoy snaking its way toward the capital, Kyiv, where air raid sirens were again ringing out on Tuesday morning.

The convoy - which seems to have slowed down in the past 24 hours - includes armoured vehicles, tanks, artillery and logistical vehicles, and is said to be less than 18 miles (30km) from Kyiv.

Nato chief Jens Stoltenberg on Tuesday accused Russian President Vladimir Putin of "shattering peace in Europe", while UK Prime Minister Boris Johnson accused Russia of "barbaric and indiscriminate practises... to send missiles into tower blocks to kill children."

"Yesterday there was very intense shelling on residential areas," said Maria Avdeeva, an international security expert who is 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.

"Already we have shortages... 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. So, I think that almost nothing is left in the shops," Ms Avdeeva, who is a research director at the European Expert Association think tank, added.

The mayor of Kherson said Russian forces had set up checkpoints surrounding the city, which has a population of some 300,000 people, and is located in the south, near Moscow-controlled Crimea.

Unverified video footage on Russian media seems to show Russian tanks rolling through the city's streets. But Mayor Igor Kolykhayev said defiantly on Facebook that the city "has been and will stay Ukrainian".

A journalist in the city, Alena Panina, told broadcaster Ukraine 24 that "the city is actually surrounded, there are a lot of Russian soldiers and military equipment on all sides".

There is still electricity, water, and heating in Kherson, Ms Panina said, but it is getting difficult to bring food into the city because it is stored in warehouses on Kherson's outskirts.

Also in the south, there were strong words from the mayor of the strategically located port city of Mariupol, who said the city had been under constant shelling.

"Russian Nazis seek the genocide of the Ukrainian nation," Vadym Boychenko told Ukrainian 24 News. "We will fight until the last bullet... If they run out, we will use our teeth against the enemy that is moving towards Mariupol."

Russian-backed separatist leader, Denis Pushilin, has said his forces will aim to encircle Mariupol on Tuesday, the Russian state-owned RIA Novosti news agency reported.

Claims that Russia is committing war crimes are mounting, with Ukraine's president, local government officials, and Amnesty International saying the attacks need 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.

Mr Khan said his investigation would look into alleged crimes arising from the fighting, as well as violations dating back to the initial Russian invasion in 2014. However any Russian nationals accused of committing war crimes, crimes against humanity or genocide in Ukraine, would have to be extradited by the Kremlin before standing trial in The Hague.

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.

On Monday, envoys for Russia and Ukraine held talks at the Belarus border on Monday, but they reached no agreements other than a commitment to meet again in the next few days.

Meanwhile Russia faced a fresh diplomatic boycott on Tuesday, when dozens of envoys from the EU, US and UK walked out of a UN human rights forum in Geneva as Russia's Foreign Minister Sergei Lavrov started giving an address via video link. He delivered a long list of grievances, from claims that the Russian language and Orthodox Church was being suppressed, to accusations that Europe was engaged in a "Russophobic frenzy".