The head of the United Nations says Ukraine has become "an epicentre of unbearable heartache and pain".
UN Secretary-General Antonio Guterres made the comment during a visit to Kyiv, just before the first Russian strike on the Ukrainian capital since Moscow's forces retreated from the city's outskirts weeks ago.
Russia pounded targets all over Ukraine on Thursday, including the attack on Kyiv that struck a residential high-rise and another building and wounded 10 people, including at least one who lost a leg, according to Ukraine's emergency services.
The bombardment came barely an hour after Ukrainian President Volodymyr Zelenskyy held a news conference with Mr Guterres, who toured some of the destruction in and around Kyiv and condemned the attacks on civilians.
Explosions were reported across the country, in Polonne in the west, Chernihiv near the border with Belarus, and Fastiv, a large railway hub south-west of the capital. The mayor of Odesa, in southern Ukraine, said rockets were intercepted by air defences.
Ukrainian authorities also reported intense Russian fire in the Donbas — the eastern industrial heartland that the Kremlin says is its main objective — and near Kharkiv, a north-eastern city outside the Donbas that is seen as key to the offensive.
In the ruined southern port city of Mariupol, Ukrainian fighters holed up in the steel plant that represents the last pocket of resistance said concentrated bombing overnight killed and wounded more people. And authorities warned that a lack of safe drinking water inside the city could lead to outbreaks of deadly diseases such as cholera and dysentery.
In Zaporizhzhia, a crucial way station for tens of thousands of Ukrainians fleeing Mariupol, an 11-year-old boy was among at least three people wounded in a rocket attack that authorities said was the first to hit a residential area in the southern city since the war began.
Vadym Vodostoyev, the boy's father, said: "It just takes one second and you're left with nothing."
Mr Guterres surveyed the destruction in small towns outside the capital that saw some of the worst horrors of the first onslaught of the war.
He condemned the atrocities committed in towns like Bucha, where evidence of mass killings of civilians was found after Russia withdrew in early April in the face of unexpectedly stiff resistance.
Battle for Donbas still raging
Kyiv has been relatively unscathed in recent weeks since Moscow refocused its efforts on the Donbas.
Getting a full picture of the unfolding battle in the east has been difficult because air strikes and artillery barrages have made it extremely dangerous for reporters to move around. Several journalists have been killed in the war, now in its third month.
Both Ukraine and the Moscow-backed rebels fighting in the east have introduced tight restrictions on reporting from the combat zone.
Western officials say the Kremlin's apparent goal is to take the Donbas by encircling and crushing Ukrainian forces from the north, south and east.
But so far, Russia's troops and their allied separatist forces appear to have made only minor gains, taking several small towns as they try to advance in relatively small groups against staunch Ukrainian resistance.
Russian military units were mauled in the abortive bid to storm Kyiv and had to regroup and refit. Some analysts say the delay in launching a full-fledged offensive may reflect a decision by Russian President Vladimir Putin to wait until his forces are ready for a decisive battle, instead of rushing in and risking another failure that could shake his rule amid worsening economic conditions at home because of Western sanctions.
Many observers suspect Mr Putin wants to be able to claim a big victory in the east by Victory Day, on May 9, one of the proudest holidays on the Russian calendar, marking the defeat of Nazi Germany during World War II.
As Russia presses its offensive, civilians again bear the brunt.
Ukraine's military said Russian troops were subjecting several places in the Donbas to "intense fire" and that over the past 24 hours, Ukrainian forces had repelled six attacks in the region.
Four civilians were killed in heavy shelling of residential areas in the Luhansk region of the Donbas, according to the regional governor.
Columns of smoke could be seen rising at different points across the Donetsk region of the Donbas, and artillery and sirens were heard on and off.
Many of the Russian troops who were in Mariupol have been leaving and moving to the north-west, a senior Pentagon official said on Thursday.
The official, who spoke on condition of anonymity to discuss the US military assessment, did not have exact numbers but said a "significant number" of the roughly one dozen battalion tactical groups that were in the city were moving out.
Russian forces are making slow, incremental progress in the Donbas — gaining only several kilometres on any given day, the official said. As of Thursday, Russia had launched about 1,900 missiles into Ukraine – the vast majority fired from outside Ukraine's borders. Most are strikes on Mariupol and the Donbas.
In Mariupol, video posted online by Ukraine's Azov Regiment inside the Azovstal steelworks showed people combing through the rubble to remove the dead and help the wounded.
The regiment said the Russians hit an improvised underground hospital and its surgery room, killing an unspecified number of people. The video could not be independently verified.
An estimated 100,000 people remained trapped in Mariupol.
Ukraine has urged its allies to send even more military equipment to fend off the Russians. US President Joe Biden asked Congress for an additional $US33 billion to help Ukraine.
AP/ABC
