Zelenskiy: "they have orders to erase us all".

A week after launching its invasion of Ukraine, Russia said its forces took control the first sizable city on Wednesday, seizing Kherson, in the south, as fighting raged around the country and Western nations tightened an economic noose around Russia.

More than half a million Ukrainians have fled the fighting since Russian President Vladimir Putin ordered a full-scale invasion of his southern neighbour nearly a week ago.

Russian bombardments of Ukrainian cities continued, with video posted on social media showing heavily damaged buildings around the second city of Kharkiv.

"While he may make gains on the battlefield, he will pay a continuing high price over the long run," U.S. President Joe Biden said at his State of the Union address. Straying from the prepared text, Biden added "He has no idea what's coming." He did not elaborate. 

The invaders' advances have been met with fierce resistance by Ukrainian forces and a miles-long Russian military convoy north of Kyiv has made little progress towards the capital.

In a video address on Wednesday, Zelenskiy said nearly 6,000 Russians had been killed in the first six days of Moscow's invasion, and that the Kremlin would not be able to take his country with bombs and air strikes.

Biden further ratcheted up sanctions on Moscow, joining the European Union and Canada in banning Russian planes from U.S. airspace.

He also said the Justice Department would seek to seize the yachts, luxury apartments and private jets of wealthy Russians with ties to Putin.

U.S. lawmakers stood, applauded and roared, many of them waving Ukrainian flags and wearing the country's blue and yellow colours, as Biden delivered his address to the chamber of the House of Representatives. 

Russian forces have taken control of Kherson, a city of nearly a quarter million people just north of Crimea, the peninsula annexed by Russia in 2014, a Russian defence ministry spokesperson said. Strategically located on the Dniepr river, the provincial capital was the biggest city to fall to Russian forces so far.

The southeast city of Mariupol had been under intense shelling since late Tuesday and was unable to evacuate wounded, according to its mayor.

A senior U.S. defense official said on Tuesday the invading force's advance on Kyiv has stalled due to logistics problems, including shortages of food and fuel, and some units appeared to have low morale. 

On Tuesday, Ukraine's leader called on Russia to stop bombarding civilians and resume talks.

"It's necessary to at least stop bombing people, just stop the bombing and then sit down at the negotiating table," Zelenskiy told Reuters and CNN in a joint interview in a heavily guarded government compound in Kyiv.

At least 21 people were killed and 112 wounded in shelling in Kharkiv in the last 24 hours, regional governor Oleg Synegubov said on Wednesday. read more

More than 450,000 people have fled Ukraine to Poland, and a further 113,000 to Romania.