LVIV, Ukraine (AP) — Russian missiles hit the city of Lviv in western Ukraine on Monday, killing at least six people, Ukrainian officials said, as Moscow’s troops stepped up strikes on infrastructure in preparation for an all-out assault on the east.

Plumes of thick, black smoke rose over the city after a series of explosions shattered windows and started fires. Lviv and the rest of western Ukraine have seen only sporadic strikes during almost two months of war and have become a relative refuge for people from parts of the country where fighting has been more intense.

Ukrainian President Volodymyr Zelenskyy, meanwhile, vowed to “fight absolutely to the end” in strategically vital Mariupol, where the last known pocket of resistance in a seven-week siege was holed up in a sprawling steel plant laced with tunnels. Russia has repeatedly urged forces there to lay down their arms, but those remaining ignored a surrender-or-die ultimatum on Sunday.

Lviv's regional governor, Maksym Kozytskyy, said six people were killed and another eight, including a child, were wounded by four Russian missile strikes. He said three hit military infrastructure facilities and one struck a tire shop. He said emergency teams were battling fires caused by the strikes.

A hotel sheltering Ukrainians who had fled fighting further east was among the buildings badly damaged in overnight missile strikes, according to Lviv Mayor Andriy Sadovyi, who put the toll at six dead and 11 wounded.

“The nightmare of war has caught up with us even in Lviv," said Lyudmila Turchak, 47, who fled with two children from the eastern city Kharkiv. "There is no longer anywhere in Ukraine where we can feel safe.”

Military analysts say Russia is increasing its strikes on weapons factories, railways and other infrastructure targets across Ukraine to wear down the country’s ability to resist a major ground offensive in the Donbas, Ukraine’s mostly Russian-speaking eastern industrial heartland.

The Russian military said missiles struck more than 20 military targets across Ukraine overnight — including ammunition depots, command headquarters and groups of troops and vehicles. Meanwhile, it said artillery hit another 315 Ukrainian targets, and warplanes conducted 108 strikes on Ukrainian troops and military equipment. The claims couldn’t be independently verified.

Gen. Richard Dannatt, a former head of the British Army, told Sky News the strikes were part of a “softening-up” campaign by Russia ahead of a planned ground offensive in the Donbas.

Russia is bent on capturing the Donbas, where Moscow-backed separatists already control some territory, after its attempt to take the capital, Kyiv, failed.

“We are doing everything to ensure the defense” of eastern Ukraine, Zelenskyy said in his nightly address to the nation on Sunday.

The looming offensive in the east, if successful, would give Russian President Vladimir Putin a badly needed victory to sell to the Russian people amid the war’s mounting casualties and the economic hardship caused by Western sanctions.

The capture of Mariupol is seen as a key step in preparations for any eastern offensive since it would free Russian troops up. The fall of the city on the Sea of Azov would hand Russia its biggest military victory of the war, giving it full control of a land corridor to the Crimean Peninsula, which it seized from Ukraine in 2014, and depriving Ukraine of a major port and prized industrial assets.

Ukrainian Deputy Defense Minister Hanna Malyar has described Mariupol as a “shield defending Ukraine."

The city has been reduced to rubble in the siege, but a few thousand fighters, by Russia's estimate, held on to the giant, 11-square-kilometer (4-square-mile) Azovstal steel mill.

“We will fight absolutely to the end, to the win, in this war,” Ukrainian Prime Minister Denys Shmyhal vowed Sunday 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.”

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

There appeared to be little hope of military rescue. Foreign Minister Dmytro Kuleba told CBS’ “Face the Nation” on Sunday that the remaining Ukrainian troops and civilians there are basically encircled. He said they “continue their struggle,” but that the city effectively doesn’t exist anymore because of massive destruction.

The relentless bombardment and street fighting in Mariupol have killed at least 21,000 people, by Ukrainian estimates. A maternity hospital was hit by a lethal Russian airstrike in the opening weeks of the war, and about 300 people were reported killed in the bombing of a theater where civilians had taken shelter.

An estimated 100,000 people remained in the city out of a prewar population of 450,000, trapped without food, water, heat or electricity.

Drone footage carried by the Russian news agency RIA-Novosti showed mile after mile of shattered buildings. Towering plumes of smoke rose from the steel complex on the city's outskirts.

Russian forces, meanwhile, carried out aerial attacks near Kyiv and elsewhere in an apparent effort to weaken Ukraine’s military capacity ahead of the anticipated assault on the Donbas.

After the humiliating sinking of the flagship of Russia’s Black Sea Fleet last week in what the Ukrainians boasted was a missile attack, the Kremlin had vowed to step up strikes on the capital.

At least five people were killed by Russian shelling in Kharkiv, Ukraine’s second-largest city, on Sunday, regional officials said. The barrage slammed into apartment buildings. The streets were littered with broken glass and other debris.

Kharkiv Mayor Igor Terekhov, in an impassioned address marking Orthodox Palm Sunday, lashed out at Russian forces for not letting up the bombing campaign on such a sacred day.

Zelenskyy called the bombing in Kharkiv “nothing but deliberate terror.”

Zelenskyy also appealed for a stronger response to what he said was the brutality of Russian troops in parts of southern Ukraine.

“Torture chambers are built there,” he said. “They abduct representatives of local governments and anyone deemed visible to local communities.”

He again urged the world to send more weapons and apply tougher sanctions against Moscow.

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Associated Press journalists around the world contributed to this report.