A view shows the bodies of civilians killed during Ukraine-Russia conflict in Mariupol, Ukraine, on Sunday. Reuters

Ukrainian authorities said missiles struck the western city of Lviv on Monday, killing six, and explosions rocked other cities as Russian forces kept up their bombardments after claiming near full control of the 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.

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.

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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 Reuters reporter 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.

A man walks near a residential building destroyed during Ukraine-Russia conflict in Mariupol, Ukraine. Reuters

Russia denies targeting civilians and has rejected what Ukraine says is evidence of atrocities as staged to undermine peace talks. It calls its action a special military operation to demilitarise Ukraine and eradicate what it calls dangerous nationalists.

Capturing the southern city would also allow Russia to fully secure a land corridor to the Crimean Peninsula, which it seized from Ukraine in 2014, and deprive Ukraine of a major port and its prized industrial assets.

As its missiles and rockets slammed into other parts of the country, Russia estimated that 2,500 Ukrainian troops and about 400 foreign mercenaries were dug in at the sprawling Azovstal steel mill, which covers more than 11 square kilometers (4 square miles) and is laced with tunnels.

Many Mariupol civilians, including children, are also sheltering at the Azovstal plant, Mikhail Vershinin, head of the city’s patrol police, told Mariupol television on Sunday. He said they are hiding from Russian shelling, and from any occupying Russian soldiers.

Service members of pro-Russian troops gather in a street in Mariupol, Ukraine, on Sunday. Reuters

Moscow had given the defenders a midday deadline to surrender and "keep their lives,” but the Ukrainians rejected it, as they've done with previous ultimatums.

"We will fight absolutely to the end, to the win, in this war,” Ukrainian Prime Minister Denys Shmyhal vowed on ABC's "This Week.” He said Ukraine is prepared to end the war through diplomacy if possible, "but we do not have intention to surrender.”

In occupied parts of the Kherson and Zaporizhzhia regions, he said, the Russians are creating separatist states and introducing Russian currency, the ruble.

Intensified Russian shelling of Ukraine’s second-largest city, Kharkiv, has killed 18 people and wounded 106 in the last four days alone, Zelensky said.

People take belongings out of a residential building in Mariupol, Ukraine, on Sunday. Reuters

"This is nothing but deliberate terror. Mortars, artillery against ordinary residential neighborhoods, against ordinary civilians,” he said.

He said a planned Russian offensive in eastern Ukraine "will begin in the near future.”

Zelensky again called for increased sanctions against Russia, including its entire banking sector and oil industry. "Everyone in Europe and America already sees Russia openly using energy to destabilize Western societies,” Zelensky said. "All of this requires greater speed from Western countries in preparing a new, powerful package of sanctions.”