The strikes hit the city, which has been spared much of the worst violence in almost two months of war, on Monday, as Ukrainian Prime Minister Denys Shmyhal vowed to “fight absolutely to the end” in strategically vital Mariupol
Plumes of thick, black smoke were rising over Lviv after the explosions, which were witnessed by Associated Press staff.
Lviv and the rest of western Ukraine have not been immune from the fighting but have been less affected than other parts of the country and considered a relative haven.
Seven people were killed and 11 wounded in overnight missile strikes, according to Lviv Mayor Andriy Sadovyi and the regional governor, Maksym Kozytskyy.
The governor said the Russian strikes hit three military infrastructure facilities and an auto mechanic shop. He said the wounded included a child, and emergency teams were battling fires caused by the strikes
A hotel sheltering Ukrainians who had fled fighting farther east was among the buildings badly damaged in the attack, the mayor said.
“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.”
A powerful explosion also rocked Vasylkiv, a town south of the capital of Kyiv that is home to a military airbase, according to residents.
Video posted on social media sites showed smoke in the area after the blast. It was not immediately clear what was hit, and there was no official confirmation from authorities.
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 Russian-speaking eastern industrial heartland.
With missiles and rockets battering various parts of the country, Mr Zelenskyy accused Russian soldiers of torture and kidnappings in areas they control.
The fall of Mariupol, which has been reduced to rubble in a seven-week siege, would give Moscow its biggest victory of the war.
But a few thousand fighters, by Russia’s estimate, were holding on to the giant, 11sq km Azovstal steel mill.
“We will fight absolutely to the end, to the win, in this war,” Ukrainian Prime Minister Denys Shmyhal vowed on ABC’s This Week on Sunday.
He said Ukraine was 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 were hiding from Russian shelling and from Russian soldiers.
Capturing the city on the Sea of Azov would free Russian troops for a new offensive to take control of the Donbas region in Ukraine’s industrial east.
Russia also would fully secure a land corridor to the Crimean Peninsula, which it seized from Ukraine in 2014, and it would deprive Ukraine of a major port and prized industrial assets.
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 defence” of eastern Ukraine, Mr Zelenskyy said in his nightly address to the nation.
As for besieged Mariupol, 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 theatre where civilians had taken shelter.
An estimated 100,000 people remained in the city out of a pre-war population of 450,000, trapped without food, water, heat or electricity.
Drone footage carried by the Russian news agency RIA-Novosti showed kilometre after kilometre of shattered buildings and, on the city’s outskirts, the steel complex, from which rose towering plumes of smoke.
Ukrainian Deputy Defence Minister Hanna Malyar described Mariupol as a “shield defending Ukraine”.
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.
Russia said on Sunday that it had attacked an ammunition plant near Kyiv overnight with precision-guided missiles, the third such strike in as many days.
Explosions were also reported in Kramatorsk, the eastern city where rockets earlier this month killed at least 57 people at a train station crowded with civilians trying to evacuate ahead of the Russian offensive.
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.
Mr Zelenskyy called the bombing in Kharkiv “nothing but deliberate terror.”
He 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.
Malyar, the Ukrainian deputy Defence Minister, said the Russians were pounding Mariupol with airstrikes and could be preparing for an amphibious landing to reinforce their ground troops.
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.
Austrian Chancellor Karl Nehammer — who met with Mr Putin in Moscow this past week in a first by a European leader since the invasion February 24 — said the Russian President is “in his own war logic” on Ukraine.
In an interview on NBC’s Meet the Press, Mr Nehammer said he thinks Putin believes he is winning the war, and “we have to look in his eyes and we have to confront him with that, what we see in Ukraine”.