KYIV (AFP, REUTERS) - The Ukrainian army said on Wednesday (March 2) that Russian airborne troops have landed in the eastern city of Kharkiv, adding that there were immediate clashes.

"Russian airborne troops landed in Kharkiv... and attacked a local hospital," the army said in a statement on messaging app Telegram. "There is an ongoing fight between the invaders and the Ukrainians."

Kharkiv, a largely Russian-speaking city near the Russian border, has a population of around 1.4 million.

It has been a target for Russian forces since President Vladimir Putin launched an invasion of Ukraine last Thursday.

In Kherson on the Black Sea, the Russian army claimed it had taken control of the southern city.

"The Russian divisions of the armed forces have taken the regional centre of Kherson under full control," defence ministry spokesman Igor Konashenkov said in televised remarks.

But in a Facebook post, Kherson’s mayor Igor Nikolayev said: "We are still Ukraine. Still firm."

Gaining control of the southern Ukrainian city of Kherson, an important port on the River Dnieper connected to the Black Sea, would be a significant coup for Russia.

The city, home to a population of 280,000 and a major ship-building industry, could serve as a strategic opening for Russian forces to make inland attacks to the west of Ukraine.

The River Dnieper is also a major water source for its surrounding land and Russian troops had already destroyed a concrete dam built in the Kherson region to cut off water to Crimea, the RIA news agency quoted Crimea's governer Sergei Aksyonov as saying last Saturday.

Ukraine cut off the fresh water supply to Crimea by damming a canal that had supplied 85 per cent of the peninsula's needs before Moscow annexed the region in 2014.

The Soviet-era canal had been built to channel water from the River Dnieper to arid areas of Kherson and Crimea.

Russia is aiming to erase Ukraine, its history and people, President Volodymyr Zelensky said in a video on Wednesday as the seventh day of Moscow’s invasion of its neighbour started with heavy shelling of the Black Sea port of Mariupol.

Moscow switched to strikes on Ukrainian cities on Tuesday and appeared poised for an advance on Kyiv as the West tightened an economic noose around Russia in retaliation.

But Mr Zelensky, unshaven and wearing a khaki T-shirt, said the West’s response was not enough, calling for more international support, including backing Ukraine’s bid to join the European Union.

"This is no time to be neutral," said Mr Zelensky, whose defiant and emotional tone in regular video addresses have offered his country support and leadership in the war, which he said killed nearly 6,000 Russian troops so far.

Referring to the Tuesday shelling in Kyiv next to Babyn Yar, the site of a World War Two massacre of tens of thousands of Jews by German occupation troops and Ukrainian auxiliaries, he said: "This strike proves that for many people in Russia our Kyiv is absolutely foreign. 

"They don’t know a thing about Kyiv, about our history. But they all have orders to erase our history, erase our country, erase us all." 

Ukraine’s south-eastern Azov Sea port of Mariupol was under constant shelling and unable to evacuate the injured while Kherson, on the Black Sea to the west, was completely surrounded by invading Russian forces, local authorities said on Wednesday.

"We all died again by Babyn Yar. Although the world has promised again and again that it will never happen again," said Mr Zelensky.

"Don’t you see what is happening? That’s why it is very important now that you, millions of Jews around the world, do not stay silent. Because Nazism is born in silence. Scream about murdering of civilians, scream about murdering of Ukrainians."

On Tuesday, officials had reported Russian checkpoints encircling the city, and Mr Nikolayev said Russian forces had taken control of the railway station and port overnight.

In a shift of tactics after its assault seemed to have stalled, Russia bombed a TV tower in Ukraine's capital on Tuesday (March 1) and rained rockets on Kharkiv as Moscow intensified its bombardment of Ukrainian urban areas.

A US official said a kilometres-long armoured column bearing down on the capital Kyiv had not made any advances in the past 24 hours, frozen in place by logistics problems, short on fuel and food, and perhaps pausing to reassess tactics.

Russia's defence ministry urged Kyiv residents to flee and said it would strike unspecified areas used by Ukraine's security services and communications. Speaking in a heavily guarded government compound in Kyiv,

Ukraine's President Zelensky said Russia must "first stop bombing people" before peace talks could make any headway.

In a joint interview with Reuters and CNN, Mr Zelensky also urged Nato members to impose a no-fly zone to stop Russia's airforce, something the military alliance has ruled out.

As he spoke, news came that a Russian missile had struck a TV tower near the Babyn Yar Holocaust memorial site in Kyiv, killing at least five people.

Mr Zelensky, who also spoke by phone for 30 minutes with US President Joe Biden on Tuesday, said the artillery barrages on Kharkiv amounted to "state terrorism".

Mr Biden and Mr Zelensky discussed how Russia had intensified attacks on sites used by civilians, the White House said.

The US president later highlighted Western unity over Ukraine in his State of the Union address. 

He added his country will join its allies and ban Russian flights from using US airspace.

Mr Biden also branded his Russian counterpart Vladimir Putin a “dictator”.

“A Russian dictator, invading a foreign country, has costs around the world,” Mr Biden told Congress. 

Mr Biden vowed that Mr Putin would pay over the long run even if he made gains on the battlefield in Ukraine.

'Shambolic'

Mr Putin has drawn global condemnation and sanctions that have already sent the rouble into freefall and forced Russians to queue outside banks for their savings.

The West has imposed heavy sanctions on Russia to shut off its economy from the global financial system, pushing international companies to halt sales, cut ties, and dump tens of billions of dollars' worth of investments.

But nearly a week since Russian troops poured over the border, they have not captured a single major Ukrainian city after running into far fiercer resistance than they expected.

"Looking at the Russian operation so far, they're having tremendous problems with logistics and communications. The whole effort seems shambolic," Michael Kofman, an expert on the Russian military at Washington's Wilson Centre, wrote in a tweet.

Many Western military analysts fear that Russia will now fall back on tactics which call for crushing bombardment of built-up areas before trying to enter them.

A senior US defence official, speaking on condition of anonymity, said: "One reason why things appear to be stalled north of Kyiv is that the Russians themselves are regrouping and rethinking and trying to adjust to the challenges that they've had."

The Russians have been surprised not only by the scale of Ukrainian resistance but also by poor morale among their own forces, some of whom surrendered without a fight, the official said, without providing evidence.

Russia still has more forces to throw into the fight, though.

Russia's Defence Minister Sergei Shoigu said the "special military operation" would continue until it had achieved its goals, defined by Putin as disarming Ukraine and capturing the "neo-Nazis" he says are running the country.

Rocket strikes on Tuesday in Kharkiv, Ukraine's second biggest city, killed at least 10 people and wounded 35, Ukrainian Interior Ministry adviser Anton Herashchenko said.

Human rights groups and Ukraine's ambassador to the United States have accused Russia of using cluster bombs and vacuum bombs, weapons condemned by many organizations. Moscow denies targeting civilians.

Munitions experts who reviewed footage on social media of attacks on Monday said Kharkiv appeared to have been targeted by cluster bombs.

High-rise buildings, schools, and kindergartens were among the buildings destroyed in those strikes, Interfax Ukraine reported, citing Ukraine's defence ministry.

In the south, Russia claimed to have completely encircled Ukraine's Azov Sea coast. If confirmed, that would mean Russian forces invading from Crimea had joined up with separatists in the east and had cut off Ukraine's main eastern port, Mariupol.

Mr Zelensky said Kyiv remained the main target. Some Kyiv residents have been sheltering in underground metro stations at night, there are long lines for fuel, and some products are running out in shops.

Appeal to Europe

In an emotional address to the European Parliament by video link on Tuesday, a day after he signed an official request to join the European Union, Mr Zelensky urged the bloc to prove that it sided with Ukraine.

"Do prove that you will not let us go. Do prove that you are indeed Europeans and then life will win over death and light will win over darkness," he said.

Russian Foreign Minister Sergei Lavrov told a Geneva disarmament meeting via video link that Ukraine had been seeking nuclear weapons. He did not provide evidence other than saying "Ukraine still has Soviet nuclear technologies and the means of delivery of such weapons."

More than 100 diplomats walked out of the hall in protest as his speech began, underlining Russia's international isolation.

Ukraine's general staff said Russian losses included 5,710 personnel, 29 destroyed and damaged aircraft and 198 tanks, all figures that could not be verified. Russia has given no full account of its battlefield losses.

'I saw war'

Moscow announced a ban on foreign companies selling assets to try to halt the flight of Western companies abandoning their Russian ties. Mr Putin also issued a decree banning cash exports of foreign currency from Russia exceeding US$10,000 (S$13,000) in value.

The rouble hit a record low on Tuesday, threatening the living standards of ordinary Russians.

More than 660,000 people, mostly women and children, have fled Ukraine to neighbouring countries such as Poland and Romania since the invasion began, the UN refugee agency said.

At the Hungarian border crossing Tiszabecs, a mother cradled a baby in her arms after a four-day drive from Kyiv.

"I saw war, I saw rockets," said her older son Ivan, 15, who looked exhausted after the journey. His father had stayed behind to fight.

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