Ukrainian authorities reported intense Russian fire in Donbas - the eastern industrial heartland that the Kremlin is bent on capturing - and near Kharkiv, a northeastern city that is outside Donbas but 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.
The fresh attacks came as the United Nations chief surveyed the destruction in small towns outside Kyiv on Thursday.
UN Secretary-General Antonio Guterres condemned the atrocities committed in towns like Bucha, where evidence of mass killings of civilians was found after Russia retreated in the face of unexpectedly stiff resistance.
"Wherever there is a war, the highest price is paid by civilians," Guterres lamented as he visited the bombed-out Kyiv suburb of Irpin.
He reiterated the importance of investigating alleged war crimes.
Many observers expect Putin will try to claim a big victory in the east by Victory Day, which marks the defeat of Nazi Germany during World War II.
Putin, like many of his predecessors, often uses patriotic Russian holidays and anniversaries to make announcements.
In March, he used a rally at a Moscow stadium to celebrate the eighth anniversary of Russia's annexation of the Crimean Peninsula, taken from Ukraine.
The discovery of the mass killings around Kyiv helped to galvanise support for Ukraine in Europe.
Bulgarian Prime Minister Kiril Petkov vowed his country would join others in providing military assistance as he toured another scene of atrocities outside Kyiv, in Borodyanka.
"We cannot be indifferent. We cannot say that this is a Ukrainian problem. We cannot say some people are dying but we are not interested in that," he said.
"This is not just the battle for Ukraine but it is a matter for civilisation to choose which side to take."
The visit by the Bulgarian leader came a day after Russia cut off the supply of natural gas to his country and fellow NATO member Poland, in what was seen as a bid to punish and divide the continent.
Satellite photos analysed by the Associated Press showed evidence of intense Russian fire on Mariupol in recent days.
A video posted online by Ukraine's Azov Regiment - a militia set up by Ukrainian ultra-nationalists in 2014 and later incorporated as a regiment in Ukraine's national guard - inside the steel plant 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.
Hundreds of thousands of Mariupol's residents have fled.
Authorities said the estimated 100,000 who remain run the risk of diseases like cholera and dysentery.
"Deadly epidemics may break out in the city due to the lack of centralised water supply and sewers," the council said on Telegram.
It reported bodies decomposing under the rubble and a "catastrophic" shortage of drinking water and food.
Russia, meanwhile, said a city under its control in the south came under fire.
In what may have been a Ukrainian counterattack, a series of explosions boomed near the television tower late on Wednesday in Kherson, which has been occupied by Russian forces since early in the war.
The blasts at least temporarily knocked Russian channels off the air.
Ukraine has urged its allies to send even more military equipment to fend off Russian forces.
US President Joe Biden plans to ask Congress for an additional $US33 billion ($A46 billion) to help Ukraine.
