The humanitarian situation was deteriorating in besieged Ukrainian cities under relentless Russian bombardment on Sunday, as Kyiv called on Moscow's ally Beijing to "condemn Russian barbarism".
In an apparent escalation of the conflict, Moscow on Saturday claimed it had used hypersonic missiles in Ukraine in what would be the first combat use of the next-generation weapons.
Thousands of people have been evacuated from besieged cities but Russian shelling was blocking efforts to deliver humanitarian supplies, President Volodymyr Zelensky said Sunday.
Aid agencies have warned they are struggling to reach hundreds of thousands of people trapped by the invading Russian forces.
A total of 6,623 people were evacuated on Saturday along humanitarian corridors, including 4,000 from the devastated southern city of Mariupol, Zelensky said in his latest video address.
Russia said Saturday its forces had broken through the defences of the besieged port and were now inside the war-torn city, which has been under relentless bombardment.
"To do such a thing to a peaceful city, what the occupiers have done, this is a terror that will be remembered even in the next century," he said.
Russian shelling also heavily damaged the Azovstal metallurgical plant in Mariupol, one of the largest in Europe, Ukrainian officials said.
"The economic losses for Ukraine are immense," tweeted lawmaker Lesia Vasylenko, who posted a video showing thick columns of smoke rising from an industrial complex.
In Mariupol, rescuers were still searching for hundreds of people trapped under the wreckage of a bombed theatre where more than 1,000 people had been seeking shelter when it was struck on Wednesday.
"This is no longer Mariupol, it's hell," said resident Tamara Kavunenko, 58. "The streets are full with the bodies of civilians."
In the encircled northern city of Chernigiv, the mayor said early Sunday that a hospital had been hit in the latest shelling.
"In Chernigiv, indiscriminate artillery shelling in residential neighbourhoods continues, killing dozens of civilians, children and women," mayor Vladislav Atroshenko said on television.
Aid agencies are struggling to reach people trapped in cities ringed by Russian forces, the UN's World Food Programme said Saturday, including hundreds of thousands of women and children.
"The challenge is to get to the cities that are encircled or about to be encircled," emergency coordinator Jakob Kern told AFP , describing the situation as "dire".
More than 3.3 million refugees have fled Ukraine, but many people have remained trapped, including "hundreds of thousands of women and children. They cannot come out and we cannot reach them," he added.
In western Ukraine, Russia claimed Saturday it had used Kinzhal (Dagger) hypersonic missiles to destroy an arms depot.
Military analyst Pavel Felgenhauer however suggested the use of the missiles would change little on the ground.
"Fundamentally this does not change anything on the battlefield, but it gives a certain psychological and propaganda effect to scare everyone," he told AFP.
Despite their progress entering the centre of Mariupol, Russian forces have met fierce resistance and been stalled outside Kyiv and several other cities in the east, making them vulnerable to Ukrainian attacks against supply lines.
In an intelligence update late Saturday, Britain's defence ministry said Ukraine was continuing to effectively defend its airspace, forcing Russia to rely on weapons launched from its own airspace.
"Gaining control of the air was one of Russia's principal objectives for the opening days of the conflict and their continued failure to do so has significantly blunted their operational progress," it tweeted.
Earlier Saturday, it said Russia had been forced to "change its operational approach and is now pursuing a strategy of attrition."
"This is likely to involve the indiscriminate use of firepower resulting in increased civilian casualties, destruction of Ukrainian infrastructure, and intensify the humanitarian crisis," it warned.
Zelensky on Saturday again appealed for peace, urging Russia to accept "meaningful" talks.
"This is the time to meet, to talk, time for renewing territorial integrity and fairness for Ukraine," he said in a video posted on social media.
Russia carried out air raids on the southern city of Mykolaiv in quick succession Saturday, Vitaly Kim, head of the regional administration, said, a day after a deadly strike on a military barracks there.
Less than 100 kilometres (62 miles) to the southeast, Ukraine claimed that a Russian general had been killed by strikes on an airfield outside Kherson, just north of Crimea. Ukraine said he was the fifth top-ranking officer killed since the invasion began on February 24.
With no apparent progress in talks with Moscow, Ukraine called on Beijing to join the West in condemning the Russian invasion, which it has so far refused.
China could play an important role in global security, top Zelensky advisor Mikhailo Podolyak tweeted Saturday, "if it makes a right decision to support the civilised countries' coalition and condemn Russian barbarism."
US President Joe Biden warned his Chinese counterpart Xi Jinping on Friday of "consequences" for any financial or military aid for Russia, a move that could turn the standoff into a global confrontation.
Xi said the war was "in no one's interest," but showed no sign of giving in to the pressure to join Western condemnation of Russia.
In New Delhi, Japanese Prime Minister Fumio Kishida on Saturday urged India to take a tougher line on Russia's invasion.
But his counterpart Narendra Modi made no direct mention of Ukraine and their joint written statement afterwards called only "for an immediate cessation of violence".
Australia meanwhile Sunday announced more sanctions against Russia, immediately banning all exports of alumina and bauxite while pledging more weapons and humanitarian assistance for Ukraine.
The export ban aims to impact aluminium production in Russia, which relies on Australia for 20 percent of its alumina.
Putin so far appears undeterred by threats and sanctions, holding a triumphalist rally in Moscow on Friday to mark eight years since Russia's seizure of Crimea, saying his goal in Ukraine was "to rid these people from their suffering and genocide."
Russia wants Ukraine to disarm and disavow all Western alliances, in particular to renounce joining Nato or to seek closer integration with the European Union — steps that Kyiv says would turn it into a vassal state of Moscow.
