Western nations are continuing to tighten an economic noose around Russia, whose invading forces have bombarded Ukrainian cities and appeared poised for an advance on Kyiv.

Hundreds of thousands of Ukrainians have fled the fighting since Putin ordered a full-scale invasion nearly a week ago, with a miles-long Russian military convoy north of Kyiv readying to advance on the capital.

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.

"While he may make gains on the battlefield - he will pay a continuing high price over the long run," US President Joe Biden said in his State of the Union address. Straying from the prepared text, Biden added "He has no idea what's coming."

Ukrainian President Volodymyr Zelenskiy 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," he told Reuters and CNN in a joint interview in a heavily guarded government compound in Kyiv.

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

The United Nations General Assembly is set to reprimand Russia on Wednesday and demand that Moscow stop fighting and withdraw its military forces.

Russia's assault included strikes on Kyiv, though the heaviest bombardment appears to be around Ukraine's second-largest city Kharkiv, near the border with Russia.

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.

West of Kyiv, in the city of Zhytomyr, four people, including a child, were killed on Tuesday by a Russian cruise missile, a Ukrainian official said.

In Ukraine's largely Russian-speaking city of Donetsk, in territory controlled by Russian-backed separatists, authorities said three civilians had been killed by Ukrainian shelling.

Sanctions on Moscow have ratched up with the US joining the European Union and Canada in banning Russian planes from their airspace. Biden also said the Justice Department would seek to seize the yachts, luxury apartments and private jets of wealthy Russians with ties to Putin.

Ukraine has called on the US-led military alliance to implement a no-fly zone over Ukraine - a request rejected by Washington, which fears stoking a direct conflict between the world's two biggest nuclear powers.

Washington and its allies have instead sent weapons to Kyiv.

The West's main strategy is shutting off Russia's economy from the global financial system, pushing international companies to halt sales, cut ties, and dump tens of billions of dollars' worth of investments.

Exxon Mobil joined other major Western energy companies including British BP PLC and Shell in announcing it would quit oil-rich Russia over the invasion.

Apple Inc stopped sales of iPhones and other products in Russia, and was making changes to its Maps app to protect civilians in Ukraine. Alphabet Inc's Google dropped Russian state publishers from its news, and Ford Motor suspended operations in the country.

US airplane manufacturer Boeing said it was suspending parts, maintenance and technical support for Russian airlines.

Russia on Tuesday placed temporary restrictions on foreigners seeking to exit Russia assets, meaning that billions of dollars worth of securities held by foreigners are at risk of being trapped.

Several dozen Japanese men have answered a Ukrainian call for foreign volunteers to fight Russia's invasion, according to a media report on Wednesday. In Taiwan, the president, vice president and prime minister all pledged to donate their salaries to Ukraine relief efforts.

Meanwhile Mexican President Andres Manuel Lopez Obrador said his country will not impose any economic sanctions and criticised wwhat he called censorship of Russian state-sponsored media by social media companies.

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