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Ukrainian President Volodymyr Zelenskyy has described Russia's rocket attack on his country's second-largest city Kharkiv as "a war crime".
He said that defending the capital Kiev's from Moscow's army was a top priority, as the Russian offensive entered its sixth day.
“The strike against Kharkiv is a war crime,” Mr Zelenskyy said in a video statement.
“This is state terrorism on the part of Russia.
“The defence of the capital today is the key priority for the state.”
At least 10 people were killed and 35 wounded on Tuesday in rocket strikes by Russian forces at the centre of Kharkiv, Interior Ministry adviser Anton Herashchenko said in a social media post.
“The rubble is being cleared and there will be even more victims and wounded,” he said.
Missiles were also used to attack the city.
Dmytro Zhyvytskyy posted photographs on the Telegram messaging service of the charred shell of a four-storey building and rescuers searching through the rubble.
In a later Facebook post, he said many Russian soldiers and some local residents were also killed during fighting in Sumy region on Sunday. The report could not be immediately confirmed.
In another development, footage circulated on social media on Monday showed the aftermath of a reported air strike on a military base in a suburb 25 kilometres north-east of Kiev.
The video showed a car passing by burning vehicles on a motorway in the city of Brovary.
Brovary city head Igor Sapozhko wrote in a Facebook post on Monday that an air strike had hit a military base in the city, killing one person and wounding five.
Russia targets residential areas in Kharkiv
Kharkiv region head Oleg Synegubov said on Tuesday that Russian rocket and missile attacks had hit the centre of the city, including residential areas and the regional administration building, as Moscow started day six of its offensive.
Mr Synegubov said Russia launched Grad rockets and cruise missiles on Kharkiv but that the city's defence was holding.
“Such attacks are genocide of the Ukrainian people, a war crime against the civilian population,” he said.
Wearing a flak jacket and a helmet, Mr Synegubov said in a video posted on social media on Tuesday morning that it was too early to know the number of casualties.
He shared a video showing the Kharkiv regional administration building being hit by a missile and exploding.
Kharkiv is about 20km south of the border with Russia. The city has been targeted with an intensifying bombardment by Russian forces.
Ukrainian authorities said at least seven people had been killed and dozens injured in fighting there. They said the actual figures could be much higher.
Russia's military operation, launched last Thursday, appears not to have achieved the decisive early gains that President Vladimir Putin would have hoped for.
Ukraine's general staff said Russian losses include 5,710 personnel, 29 destroyed and damaged aircraft and 198 tanks.
It is not possible to independently verify these figures.
Ceasefire talks between Russia and Ukraine held on Monday failed to reach a breakthrough and negotiators have not said when a new round will take place.
Russian President Vladimir Putin faces mounting international pressure and the systemic impact of Western sanctions led to a near 30 per cent collapse in the rouble on Monday, before central bank intervention rescued the currency from its lows.
The US and its allies have sought to punish Russia economically for staging the biggest assault on a European state since the Second World War.
They have imposed sanctions on Russia's top businesses, oligarchs and officials, including Mr Putin.
Ukraine seeks nuclear-safe zones
The head of Ukraine’s nuclear power utility called on international monitors to intervene to ensure the safety of the country’s 15 atomic reactors, as advancing Russians near Europe’s largest nuclear plant.
The International Atomic Energy Agency will convene an emergency session on Wednesday in Austrian capital Vienna to assess the situation. The watchdog has been warning for days that the war threatens to trigger a wider tragedy by damaging nuclear power infrastructure.
“I continue to follow developments in Ukraine very closely and with grave concern, especially the conflict’s potential impact on the safety and security of the country’s nuclear facilities,” IAEA director general Rafael Mariano Grossi said late on Monday.
“It is extremely important that the nuclear power plants are not put at risk in any way. An accident involving the nuclear facilities in Ukraine could have severe consequences for public health and the environment.”