Ukraine acknowledged on Friday it was taking heavy losses in Russia's assault in the east, but said Russia's losses were even worse, as U.S. President Joe Biden called on Congress to send as much as $33 billion to help Kyiv withstand the attack.

President Volodymyr Zelenskiy praised Biden's offer of help, which amounts to nearly 10 times the aid Washington has sent so far since the war began on Feb. 24.

In Kyiv, workers were cleaning up rubble in a residential area after Russia fired two missiles at the capital during a visit on Thursday by U.N. Secretary-General Antonio Guterres, which Ukraine called an attack on the United Nations itself.

Having failed in an assault on Kyiv in the north of Ukraine last month, Russia is now trying to fully capture two eastern provinces known as the Donbas.

Ukraine has acknowledged losing control of some towns and villages there since the assault began last week, but says Moscow's gains have come at a massive cost to a Russian force already worn down from its earlier defeat near the capital.

"We have serious losses but the Russians' losses are much much bigger...They have colossal losses," presidential adviser Oleksiy Arestovych said.

By pledging tens of billions of dollars in aid for Ukraine, Biden has dramatically increased U.S. involvement in the conflict. The United States and its allies are now sending heavy weapons including artillery, with what Washington says is an aim not just to repel Russia's attack but to weaken its armed forces so it cannot menace its neighbours again.

"We need this bill to support Ukraine in its fight for freedom," Biden said. "The cost of this fight - it's not cheap - but caving to aggression is going to be more costly."

Zelensky tweeted: "Thank you @POTUS and the American people for their leadership in supporting Ukraine in our fight against Russian aggression. We defend common values - democracy and freedom. We appreciate the help. Today it is needed more than ever!"

Russia has said the arrival of Western arms into Ukraine means it is now fighting a "proxy war" against NATO. President Vladimir Putin threatened unspecified retaliation this week, while his foreign minister warned of a threat of nuclear war.

Zelensky's office said Russia was pounding the entire front line in the eastern Donetsk region with rockets, artillery, mortar bombs and aircraft. The Ukrainian general staff said Russia was shelling positions along the line of contact to prevent the Ukrainians from regrouping.

Britain said fighting had been particularly heavy around the cities of Lysychansk and Severodonetsk, the main part of the Donbas that Russia is still trying to capture, with an attempted advance south from Russian-held Izium towards Sloviansk.

"Due to strong Ukrainian resistance, Russian territorial gains have been limited and achieved at significant cost to Russian forces," the British defence ministry said in an update.

The bloodiest fighting and worst humanitarian catastrophe of the war have been in Mariupol, an eastern port reduced to a wasteland by two months of Russian bombardment and siege.

Ukraine says 100,000 civilians are still in the city, which is mostly occupied by Russia. Hundreds of civilians are holed up with last remaining defenders in underground bunkers beneath a huge steel works.

Zelenskiy's office said an operation was planned on Friday to get civilians out of the plant, giving no details.

In the capital, normal life has largely returned after weeks in which residents were forced to shelter in metro stations from bombardment. The front line, which come right to the outskirts of Kyiv in March, is now hundreds of miles away. Foreign dignitaries have been flying in to pay their respects to Zelenskiy and his government.

But Russia can still hit the city with long range missiles, as it did on Thursday, during a visit by U.N. Secretary-General Guterres, in what Ukrainian Defence Minister Oleksiy Reznikov called "an attack on the security of the Secretary General and on world security".

No one was killed but at least four people were wounded in the missile strike in the capital, which blew out windows and scattered rubble across the streets.

"Kyiv is still a dangerous place and Kyiv is still the target of Russians, of course. The capital of Ukraine is the goal and they want to occupy it," Mayor Vitali Klitschko said, supervising the cleanup.

On Thursday, Guterres visited Borodianka, one of the Kyiv suburbs that Russia had occupied in March, leaving dead bodies in the ruined streets when its forces withdrew.

"I imagine my family in one of those homes, now destroyed and black. I see my granddaughters running away in panic, part of the family eventually killed," Guterres told reporters in Borodianka, surrounded by scorched, windowless apartment blocks.

"Innocent civilians were living in these buildings, they were paying the highest price for a war which they have not contributed to at all."