The United States led a Western assault on Moscow's economic lifeline Tuesday, banning imports of Russian oil as civilians fled besieged Ukrainian cities in a desperate evacuation push blighted by Russian shelling.

President Joe Biden heralded the US embargo as a hit on "the main artery of Russia's economy" targeting President Vladimir Putin's most crucial source of revenue -- and vowed Ukraine would "never be a victory" for Putin.

As the invasion approached its third week, Britain said it would phase out Russian oil by year's end while oil giants BP and Shell announced an immediate halt to Russian oil and gas purchases and the European Union planned to slash gas imports by two-thirds.

The latest Western strike at Russia's economy came as the United Nations said more than two million civilians have flooded across Ukraine's borders to escape towns devastated by shelling and airstrikes, in Europe's fastest-growing refugee crisis since World War II.

After days of heavy fighting in the northern city of Sumy, the first convoy of 22 buses evacuating families along a humanitarian corridor arrived in central Ukraine under a deal with Moscow to hold fire in cities targeted by its forces, with a second convoy on the way.

Kyiv said 21 people, including two children, had been killed in airstrikes in Sumy on Monday.

Attempted evacuations from the blockaded port town of Mariupol -- where aid workers said tens of thousands were living in "apocalyptic" conditions -- have failed on several occasions however, with Kyiv accusing Moscow of attacking fleeing civilians in an act of "genocide".

Authorities in the southern hub, which has had no water, power or heating since Friday, said a six-year-old girl identified only as Tanya died from dehydration under the rubble of her destroyed home.

"In the last minutes of her life she was alone, exhausted, frightened and terribly thirsty," Mayor Vadym Boychenko said on the city's Telegram channel.

- 'Nobody left' -

In a defiant speech to British lawmakers, Ukraine's President Volodymyr Zelensky invoked Winston Churchill's resistance against Nazi Germany as he vowed to "fight to the end."

"We will fight in the forests, in the fields, on the shores, in the streets," he told the packed chamber, which gave him a standing ovation.

But he complained he was not receiving desperately needed air support.

Governments on both sides of the Atlantic have balked at the idea of a no-fly zone to defend Ukraine's skies, with Putin warning it would be considered as "participation in the conflict" with nuclear-armed Russia.

Poland said Tuesday it was "ready" to hand its MiG-29 fighter jets to the United States, under a scheme that would see the planes sent to Ukraine via a US air base.

But the United States rejected the Polish offer as not "tenable," saying it raised "serious concerns" for the entire NATO alliance.

The Pentagon estimated that between 2,000 and 4,000 Russian soldiers had been killed so far. Russia said on March 2 that 498 Russian troops had been killed in Ukraine.

Russian troops are slowly encroaching on Kyiv despite intense efforts by outgunned Ukrainian forces, and moving faster through the east and north of the country.

Despite the sound of nearby shelling in the suburb of Irpin, seen as a critical point for the advance on the capital, civilians fled in icy wind and thick snowfall, AFP reporters witnessed.

People waited in a long line to cross over the Irpin river on makeshift walkways of planks and mangled metal, after the Ukrainians blew up the bridge leading into the capital to hamper any Russian advance.

"I didn't want to leave, but there's nobody left in the homes around us, no water, no gas and no electricity," Larissa Prokopets, 43, told AFP.

- 'Someone could kill him' -

Many of Kyiv's men have joined the military, leaving thousands of women to raise young children alone, some spending their nights sheltering from bombing in the concrete tunnels of the underground metro system.

According to the UN Population Fund, 81 babies were born in Kyiv's bunkers and makeshift bomb shelters at the weekend, five of them in metro stations.

Taria Blazhevych, a 27-year-old mother of two boys aged under six, told AFP she hoped her children had no real grasp of the horror of their situation.

"I tell them that all will be good, that their father will come back for them, but they understand that someone could kill him or shoot him," she said.

On Tuesday evening to the northwest of Kyiv, Ukrainian emergency services said an airstrike in the town of Malyn destroyed seven houses and killed five people including two babies born last year.

Russia's assault on its ex-Soviet neighbour and the plight of civilians caught up in the bloodshed has fueled global outrage.

At least 474 civilians have been killed so far, according to the United Nations, although it believes the real figures to be "considerably higher".

The onslaught has created a huge refugee crisis for European countries that have taken in Ukrainians fleeing the conflict, particularly Poland.

"It doesn't stop," Filippo Grandi, the UN High Commissioner for Refugees, said as he announced that two million people had fled.

As Western nations look to tighten the economic screws on Moscow, faced with the snowballing humanitarian crisis, Russia has warned that oil sanctions would have "catastrophic consequences".

But the United States led the push -- partly because Russia accounts for less than 10 percent of US oil and petroleum imports, making the impact on the world's largest economy easier to bear.

Biden said the United States -- which last year imported $17.5 billion in crude, fuel oil and petroleum products from Russia, according to census data -- decided the ban "in close consultation" with allies, especially in Europe, who depend on Russia for 40 percent of their gas needs.

US Undersecretary of State for Political Affairs Victoria Nuland separately told lawmakers that the Nord Stream 2 pipeline -- the Kremlin's prize energy project that became a victim of Western sanctions -- was "dead" and would not be revived.

With the growing raft of Western sanctions beginning to bite, ratings agency Fitch downgraded Russia deep into junk territory on Tuesday, predicting a sovereign default to be "imminent."

The pressure has grown day by day on businesses and sports to sever ties with Moscow. 

The Premier League announced it would suspend its deal with its Russian broadcast partner, while Coca-Cola, McDonald's and Starbucks joined the exodus of companies from Russia on Tuesday. 

Ukraine not to insist on NATO membership

President Volodymyr Zelensky said he is no longer pressing for NATO membership for Ukraine, a delicate issue that was one of Russia's stated reasons for invading its pro-Western neighbor.

In another apparent nod aimed at placating Moscow, Zelensky said he is open to "compromise" on the status of two breakaway pro-Russian territories that President Vladimir Putin recognized as independent just before unleashing the invasion on February 24.

"I have cooled down regarding this question a long time ago after we understood that ... NATO is not prepared to accept Ukraine," Zelensky said in an interview aired Monday night on ABC News.

"The alliance is afraid of controversial things, and confrontation with Russia," the president added.

Referring to NATO membership, Zelensky said through an interpreter that he does not want to be president of a "country which is begging something on its knees." 

Russia has said it does not want neighboring Ukraine to join NATO, the transatlantic alliance created at the start of the Cold War to protect Europe from the Soviet Union. 

In more recent years the alliance has expanded further and further east to take in former Soviet bloc countries, infuriating the Kremlin.

Russia sees NATO enlargement as a threat, as it does the military posture of these new Western allies on its doorstep.

Shortly before he shocked the world by ordering the invasion of Ukraine, Putin recognized as independent two separatist pro-Russian "republics" in eastern Ukraine -- Donetsk and Lugansk -- that have been at war with Kyiv since 2014. 

Putin now wants Ukraine, too, to recognize them as sovereign and independent.

When ABC asked him about this Russian demand, Zelensky said he was open to dialogue.

"I'm talking about security guarantees," he said.

He said these two regions "have not been recognized by anyone but Russia, these pseudo republics. But we can discuss and find the compromise on how these territories will live on."

"What is important to me is how the people in those territories are going to live who want to be part of Ukraine, who in Ukraine will say that they want to have them in," Zelensky said.

"So the question is more difficult than simply acknowledging them," the president said.

"This is another ultimatum and we are not prepared for ultimatums. What needs to be done is for President Putin to start talking, start the dialogue instead of living in the informational bubble without oxygen."

US rejects Poland offer of jets

The United States on Tuesday rejected a Polish offer to send MiG-29 fighter jets to Ukraine via a US air base, saying the proposal raised "serious concerns" for the entire NATO alliance.

Warsaw caught US officials off guard with the offer to deliver the Soviet-era planes to the US base in Ramstein, Germany. 

Under the proposed scheme, those jets could then be deployed to Ukraine, while the Polish air force would receive F-16 fighters as replacements.

Pentagon spokesman John Kirby said the prospect of the jets, placed at the disposal of the United States, flying from a US-NATO base "into airspace that is contested with Russia over Ukraine raises serious concerns for the entire NATO alliance."

"We will continue to consult with Poland and our other NATO allies about this issue and the difficult logistical challenges it presents, but we do not believe Poland's proposal is a tenable one," Kirby said in a statement.

"It is simply not clear to us that there is a substantive rationale for it," he added. 

Kirby also stressed that Washington's stance was that "the decision about whether to transfer Polish-owned planes to Ukraine is ultimately one for the Polish government."

Ukraine has stepped up calls for Western allies to supply it with military jets in the face of the Russian invasion, but providing Kyiv with war planes poses serious risks -- with NATO members unwilling to be deemed co-combatants by Moscow.

Ukraine's air force fleet consists of aging Soviet-era MiG-29 and Sukhoi-27 jets, and heavier Sukhoi-25 jets -- and these are the only planes Ukrainian pilots could fly immediately without additional training.

US Secretary of State Antony Blinken said during a visit to Moldova on Sunday that Washington was "actively" looking at a deal with Poland to provide Ukraine with the MiG-29s.

But after Poland announced its offer, US Undersecretary of State for Political Affairs Victoria Nuland told US lawmakers that Washington had been caught off guard.

Asked by a senator whether US officials coordinated ahead of time with Warsaw, Nuland said: "Not to my knowledge."

While several lawmakers pressed for the jets to be rushed to Ukraine, Nuland refused to commit Washington to supporting or facilitating the exchange.

"I will continue to convey the very strong bipartisan view of this committee that these planes need to get to Ukraine," she told the panel.

"There are a number of factors to consider here and there are some mixed views among allies and even within the administration." 

While a significant part of Ukraine's air force remains intact since the war began on February 24, both Ukraine and Russia have sustained significant losses and neither controls the airspace over the country.