Ukrainian authorities said missiles struck Lviv early on Monday and explosions rocked other cities as Russian forces kept up their bombardments after claiming near full control of the strategic southern port of Mariupol.
Driven back by Ukrainian resistance in the north, the Russian military has refocused its ground offensive in the two eastern provinces known as the Donbas, while launching long-distance strikes at other targets, including the capital, Kyiv, reports Reuters.
Capturing Mariupol would be a huge strategic prize for Russia, linking territory held by pro-Russian separatists in the east with the Crimea region Moscow annexed in 2014.
Lviv regional governor Maksym Kozystkiy said missiles struck military facilities and a car tire service point.
The city's mayor, Andriy Sadoviy, said in addition to the six killed, eleven were wounded and the blast had shattered the windows of a hotel housing Ukrainians evacuated from elsewhere in the country.
In Kyiv, a witness heard a series of blasts near the Dnipro river, while media outlet Suspilne said two people were wounded in attacks in the southern region of Dnipropetrovsk.
Russia denies targeting civilians and has rejected what Ukraine says is evidence of atrocities as staged to undermine peace talks.
It calls its action, launched almost two months ago, a special military operation to demilitarise Ukraine and eradicate what it calls dangerous nationalists.
The West and Kyiv accuse Russian President Vladimir Putin of unprovoked aggression.
On Monday, Russia's defence ministry said it had destroyed four arms and military equipment depots in Ukraine overnight and hit 315 Ukrainian targets, the TASS news agency reported.
BATTLE FOR MARIUPOL
Ukrainian Prime Minister Denys Shmyhal said troops in the pulverised port of Mariupol were still fighting on Sunday, despite a Russian demand to surrender.
"The city still has not fallen," he told ABC's "This Week" programme, adding that Ukrainian soldiers continued to control some parts of the southeastern city.
On Saturday, Russia said it had control of urban areas, though some Ukrainian fighters remained in the Azovstal steelworks, one of Europe's biggest metallurgical plants, which sprawl more than 11 sq km (4.25 sq miles) and overlook the Sea of Azov.
On the eve of the war, Mariupol was the biggest city still held by Ukrainian authorities in the Donbas, which Moscow has demanded that Ukraine cede to pro-Russian separatists.
It would unite Russian forces on two of the main axes of the invasion, and free them up to join an expected new offensive against the main Ukrainian force in the east.
On the streets of Mariupol, small groups of bodies were lined up under colourful blankets, surrounded by shredded trees and scorched buildings.
Residents, some pushing bicycles, picked their way around destroyed tanks and civilian vehicles while Russian soldiers checked the documents of motorists.
One resident, Irina, was evacuating with a niece wounded in the shelling.
"I hope they will re-build (Mariupol). The most important thing is utility systems. Summer will pass fast and in winter it will be hard," she said.
Serhiy Gaidai, the governor of the Luhansk region, said street fighting had begun between Ukrainian and Russian troops and repeated a plea for people to evacuate.
Russians had advanced overnight and taken Kreminna, he said in a televised speech, adding that authorities could no longer take people out of the town.
"The next week will be difficult," he said in an earlier post on his Facebook page. "It may be the last time we have a chance to save you."
About four million Ukrainians have fled the country, cities have been shattered and thousands have died since the start of the invasion on Feb 24.
The economic damage is significant. Shmyhal said Ukraine's budget deficit was about $5 billion a month and urged Western governments for more financial aid.
On Twitter, Ukraine President Volodymyr Zelensky said he had discussed ensuring his country's financial stability and preparations for post-war reconstruction with International Monetary Fund Managing Director Kristalina Georgieva.
He quoted her as having said support was essential to lay the foundations for rebuilding. Ukraine pressed on with efforts to swiftly join the European Union, as officials completed a questionnaire that is a starting point for the EU to decide on membership.
