Russian forces pressed their offensive in south and east Ukraine on Friday after bombarding its capital during a visit by the United Nations' chief.
At least three people were wounded in strikes late Thursday in the western part of Kyiv, the first in the capital in nearly two weeks, which came after Guterres toured Bucha and other suburbs where Moscow is alleged to have committed war crimes.
Three months into an invasion that failed in its short-term aim of capturing Kyiv, Russia is now intensifying operations in the breakaway eastern Donbas region, as Ukraine's Western allies supply it with increasingly heavy armaments.
After Moscow's retreat from Kyiv, dozens of bodies in civilian clothes were found and Ukrainian prosecutors said they have opened investigations into 10 Russian soldiers for suspected atrocities in Bucha and pinpointed more than 8,000 alleged war crimes cases.
Those cases involve "killing civilians, bombing of civilian infrastructure, torture" and "sexual crimes" reported during Russia's occupation of various parts of Ukraine, prosecutor general Iryna Venediktova told a German TV channel.
In Washington, President Joe Biden on Thursday urged US lawmakers to approve a huge $33 billion aid package and proposed new laws to allow using luxury assets stripped from Russian oligarchs to compensate Ukraine for damage inflicted since Moscow invaded on February 24.
"The cost of this fight is not cheap. But caving to aggression is going to be more costly if we allow it to happen," Biden said.
Ukrainian President Volodymyr Zelensky hailed Biden's proposal as an "important step" and "necessary."
- 'Shocking' -
In a residential part of Kyiv, AFP correspondents saw one building in flames and black smoke pouring into the air after the Russian strikes.
"I heard the sound of two rockets and two explosions. It was a sound similar to a flying plane, and then two explosions with an interval of three to four seconds," Oleksandr Stroganov, 34, told AFP.
Mayor Vitali Klitschko said there had been "two hits in the Shevchenkovsky district", with one hitting "the lower floors of a residential building". Three people were taken to hospital, but the extent of their injuries was not immediately clear.
"It is a war zone, but it is shocking that it happened close to us," Saviano Abreu, spokesman for the UN's humanitarian office who was travelling with Guterres, told AFP, adding the delegation was safe.
Zelensky said the strikes, which came immediately after his talks with Guterres, were an attempt by Russia "to humiliate the UN and everything that the organisation represents."
A Russian military spokesman told reporters that Moscow's army had conducted air strikes against 38 military targets, but made no immediate mention of Kyiv or the region around the capital.
Guterres, who arrived in Kyiv after talks in Moscow with Russian President Vladimir Putin, called the war "evil" after visiting Bucha and demanded the Kremlin cooperate with an International Criminal Court investigation into the accusations.
Prosecutors said the 10 servicemen under investigation are suspected of "premeditated murder", cruel treatment and other violations of the laws and customs of war during their occupation of Bucha, northwest of Kyiv.
At a joint press conference with Zelensky, Guterres admitted the UN Security Council had "failed to do everything in its power to prevent and end this war."
"This is the source of great disappointment, frustration and anger", he added.
- 'Idle comments' -
In Washington, Biden pushed back against increasingly heated claims by Russian officials that Moscow is fighting the entire West, rather than only Ukraine.
"We're not attacking Russia. We are helping Ukraine defend itself against Russian aggression," Biden said.
The US leader also blasted Moscow for "idle comments" on the possible use of nuclear weapons.
The $33 billion package sought by Biden is a significant increase on previous requests.
The bulk -- $20 billion -- would be weapons and other security assistance, while $8.5 billion will be economic aid.
A senior US official, speaking on condition of anonymity, said the spending package would keep Ukraine's government and military going through the start of October.
While Biden noted the US was sending 10 anti-tank weapons for every Russian tank, Ukraine's air force commander said his country's anti-aircraft systems were unable to strike bombers flying at altitudes of eight kilometres and higher.
"We need medium and long-range anti-aircraft systems" and "modern fighters", said Mykola Olechchuk.
Russia has targeted Western-supplied arms, as the United States and Europe increasingly heed Zelensky's call for heavier firepower, despite misgivings about being drawn into a conflict with Moscow.
The German parliament on Thursday voted overwhelmingly in favour of providing Kyiv with heavy weapons, a major shift in policy.
In its economic standoff with the West, Russia on Wednesday cut gas supplies to Bulgaria and Poland. Both are now receiving gas from European Union neighbours.
On Thursday, Bulgaria's Prime Minister Kiril Petkov urged Europe to be "stronger" and wean itself off Russian gas.
- 'Apocalpyse' -
With the war claiming thousands of lives, Kyiv has admitted Russian forces are making gains in the east, capturing a string of villages in the Donbas region.
The first phase of Russia's invasion failed to reach Kyiv or overthrow the government after encountering stiff resistance reinforced with Western weapons.
The Russian campaign has since refocused on seizing the east and south of the country while using long-range missiles against west and central Ukraine.
Guterres said the UN was doing everything possible to evacuate civilians from the "apocalypse" in the besieged port city of Mariupol.
In an early morning statement on Telegram, defenders of the Azovstal factory there said shelling had struck a field hospital inside the plant, causing it to collapse.
"Among the already wounded servicemen are dead, newly wounded and injured," the statement said without providing specific casualty numbers.
In Kharkiv, local Governor Oleh Synegubov said five civilians were killed Thursday in what he described as near-continuous shelling.
More than 2,000 buildings in the city have been damaged or destroyed by fire since Russia launched its invasion, leaving its firefighters at the breaking point.
"Two weeks ago there was a big shelling in the city centre and 56 fire trucks went in to extinguish different areas... a lot of apartments were bombed," Roman Kachanov, a firefighter who heads the N11 fire station told AFP.
"And this has been going on day after day and people don't have enough time to rest," he said. "It's exhausting, you're just as tired as hell."
- 'Only one hope' -
A Russian official, meanwhile, said Thursday that the ruble will soon be introduced in areas of Ukraine under Moscow's control, despite Russia earlier insisting it was not seeking to occupy captured territory.
Ukraine's ombudsman condemned the move as "act of annexation" and "gross violation" of UN Charter articles.
Nearly 5.4 million Ukrainians have fled their country since the invasion, according to the United Nations, and more than 12 million others are displaced internally.
"We feel bad, we shouldn't be standing here," Svitlana Gordienko, a nurse forced to relocate to the southern city of Zaporizhzhia, told AFP as she queued for food at a humanitarian hub.
"We're left with only one hope: to return home," added pensioner Galina Bodnya.