Russian forces shelled several Ukrainian cities on Wednesday as troops battled in the streets of Kharkiv and Ukraine's president accused Moscow of wanting to "erase our country".

Russia also said it had captured the Black Sea port of Kherson on the seventh day of Moscow's invasion, while Russian artillery massed outside the capital Kyiv -- raising fears of an imminent assault.

Several victims were reported killed by the shelling in southern and eastern Ukraine, adding to a civilian death toll of at least 350 people, including 14 children, according to Ukrainian authorities.

Russia has defied massive economic and diplomatic sanctions and growing global isolation to push on into pro-Western Ukraine, where its forces have encountered stiff resistance.

AFP saw the aftermath of apparent Russian bombing on a market and a residential area in Zhytomyr, around 150 kilometres (93 miles) from Kyiv, and in Kharkiv, Ukraine's second biggest city.

"There is nowhere in Kharkiv where shells have not yet struck," said Anton Gerashchenko, an adviser to Ukraine's interior minister, after Russian airborne troops landed in the city before dawn.

In Kyiv, mayor Vitali Klitschko said that "the enemy is drawing up forces closer to the capital".

"Kyiv is holding and will hold. We are going to fight," the former champion boxer added.

Many residents have been hunkered down for a week and dozens of families could be seen sheltering on Wednesday in the Dorohozhychi metro station.

"What happens to us down here when the food runs out? Do we try to get out and run?" said Volodymyr Dovgan, a 40-year-old IT engineer.

- Possible talks? -

With the international community piling pressure on Russia to halt the conflict, the Kremlin said a Russian delegation would be ready to meet Ukrainian officials at an undisclosed location on Wednesday.

A Ukrainian delegation member, David Arakhamia, said there would be talks but did not specify a place, date or time.

Ukrainian Foreign Minister Dmytro Kuleba said Ukraine would not hear Russian "ultimatums".

Initial talks on Monday between Russia and Ukraine failed to yield any breakthroughs.

In a video address on Wednesday, Ukraine's President Volodymyr Zelensky said Russian forces wanted to "erase our country, erase us all".

The leader said Tuesday's strike on a television mast in the capital Kyiv demonstrated Russia's threat to Ukrainian identity.

Five people were killed in the attack on the tower at Babi Yar, the site of a Nazi massacre in which over 33,000 people were killed -- most of them Jews.

The 44-year-old Zelensky, who is himself Jewish, urged Jewish people around the world to speak up.

"Nazism is born in silence. So, shout about killings of civilians. Shout about the murders of Ukrainians," he said.

In his first State of the Union address on Tuesday, US President Joe Biden called Russian President Vladimir Putin a "dictator" and warned of more sanctions to cripple Russia's economy.

Russian troops rolled into Ukraine last week to achieve Putin's mission of overthrowing Zelensky's government and "denazifying" the pro-Western country.

The UN said nearly 875,000 people have fled since the conflict began, including thousands of students and migrant workers from Africa and the Middle East who had been living in Ukraine.

"We left everything there as they came and ruined our lives," said Svitlana Mostepanenko, a refugee registering in Prague.

- 'The city will die' -

While Ukrainian forces have held Russian forces back from the country's main cities, the Russian army said it was now in "full control" of Kherson, a city with a population of 290,000 people.

The claim was not confirmed by Kherson mayor Igor Nikolayev who appealed on Facebook for permission to transport the dead and wounded out of the city and for food and medicine to be allowed in.

"Without all this, the city will die," he wrote.

Ukraine's army also said there was a fierce battle under way in Kharkiv, in northeast Ukraine near the Russian border with a population of 1.4 million.

"There is an ongoing fight between the invaders and the Ukrainians," the army said on the messaging app Telegram.

Firefighters work to contain a fire in the complex of buildings housing the Kharkiv regional SBU security service and the regional police. Photo: AFPFirefighters work to contain a fire in the complex of buildings housing the Kharkiv regional SBU security service and the regional police. Photo: AFP

Shelling in Kharkiv on Tuesday drew comparisons to the massacres of civilians in Sarajevo in the 1990s and condemnation for what Zelensky called a "war crime".

The city of Mariupol on the Azov Sea was also reportedly encircled by Russian forces.

In an important strategic victory, Russian troops attacking from the Crimean peninsula said they had linked up along the Azov Sea coast with pro-Moscow separatists in eastern Ukraine.

The separatists have been fighting Ukrainian government forces since 2014 in a conflict that has killed more than 14,000 people.

As the civilian death toll mounts, there is growing opposition to the conflict within Russia, with thousands detained for taking part in anti-war protests.

"I am urging everyone to take to the streets and fight for peace," jailed Kremlin critic Alexei Navalny said in a statement posted on Facebook.

He called on Russians not to be afraid of going to prison.

"Everything has a price and now, in the spring of 2022, we should pay that price."

- 'Russia will be a pariah' -

Western countries have imposed heavy sanctions on Russia's economy and there have been international bans and boycotts against Russia in everything from finance to tech, from sports to the arts.

In the latest development, the EU banned broadcasts of Russian state media RT and Sputnik and excluded seven Russian banks from the global SWIFT bank messaging system.

The list did not name two major Russian banks, Sberbank and Gazprombank, which were left connected to SWIFT to allow EU countries to pay for Russian gas and oil deliveries.

Ukrainian soldiers carry water supplies near a military base in Lviv. Photo: AFPUkrainian soldiers carry water supplies near a military base in Lviv. Photo: AFP

EU and NATO members have also sent arms and ammunition to Ukraine, although they have made clear that they will not send troops and the EU has dampened Zelensky's hopes of membership of the bloc.

In response to the invasion, Western companies have pulled out of projects in Russia, deepening the economic toll on Moscow that saw the ruble collapse this week.

German logistics giant DHL was one of the latest to announce a ban, saying it would stop deliveries to Russia and neighbouring Belarus, which has allowed the passage of Russian troops to attack Ukraine.

"Going forward, Russia will be a pariah, and it's hard to see how they can restore anything resembling normal interactions in the international system," said Sarah Kreps, professor at Cornell University.

The invasion has sent global markets into a spiral, with crude surging past $110 a barrel Wednesday and equities sinking.

Aluminium and gas prices hit record highs on supply fears and the Moscow Stock Exchange failed to open for a third day running.

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