LVIV, Ukraine (AP) — Russian forces launched missile attacks on the western city of Lviv and pounded a multitude of other targets across Ukraine on Monday in what appeared to be an intensified bid to grind down the country’s defences ahead of an all-out assault on the east.

At least seven people were reported killed in Lviv, where plumes of black smoke rose over a city that has seen only sporadic attacks during almost two months of war and has become a haven for civilians fleeing the fighting elsewhere. To the Kremlin’s increasing anger, Lviv has also become a major gateway for NATO-supplied weapons and foreign fighters joining the Ukrainian cause.

The attacks came as Russia continued building up troops and artillery in the east and south for the expected start of a new ground offensive in the Donbas, Ukraine’s mostly Russian-speaking industrial heartland.

In other developments, a few thousand Ukrainian troops, by Russia’s estimate, remained holed up at a mammoth steel mill in Mariupol, the last known pocket of resistance in the devastated southern port city after seven weeks of bombardment. The holdouts ignored a surrender ultimatum from the Russians on Sunday.

And Ukrainian President Volodymyr Zelenskyy submitted a filled-out questionnaire in the first step toward obtaining accelerated membership in the European Union — a desire that has been a source of irritation to Russia for years. Zelenskyy, though, has offered to drop any effort to join NATO, one of the Kremlin’s key demands.

The Russian missile strikes on Lviv hit three military infrastructure facilities and an auto mechanic shop, according to the region’s governor, Maksym Kozytskyy. He said the wounded included a child.

Lviv, the biggest city and a major transportation hub in western Ukraine, is about 80 kilometres (50 miles) from Poland, a NATO member.

Russia has strongly complained about the increasing flow of Western weapons to Ukraine. On Russian state media, some anchors have charged that the supplies amount to direct Western engagement in the fight against Russia.

Lviv has also been seen as a relatively safe place for the elderly, mothers and children trying to escape the war. A hotel sheltering Ukrainians who had fled fighting in other parts of the country was among the buildings badly damaged, Mayor Andriy Sadovyi said.

“The nightmare of war has caught up with us even in Lviv,” said Lyudmila Turchak, who fled with two children from the eastern city of 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 air base, according to residents. It was not immediately clear what was struck.

Kharkiv, Ukraine’s second-largest city, was hit by shelling that killed at least three people, according to Associated Press journalists on the scene. One of the dead was a woman who appeared to be going out to collect water in the rain. She was found lying with a water canister and an umbrella by her side.

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 offensive in the Donbas, whose capture has become the Kremlin’s main goal since its attempt to storm Kyiv failed.

The Russian military said its missiles struck more than 20 military targets in eastern and central Ukraine in the past day, including ammunition depots, command headquarters and groups of troops and vehicles.

It also reported that its artillery hit an additional 315 Ukrainian targets and that warplanes conducted 108 strikes on Ukrainian troops and military equipment. The claims could not be independently verified.

Over the weekend, Russia also claimed to have destroyed Ukrainian air defence radar equipment.

Gen Richard Dannatt, a former head of the British Army, told Sky News that Russia is waging a “softening-up” campaign ahead of the Donbas offensive.

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

A senior US defence official, speaking on condition of anonymity to discuss internal assessments of the war, said there are now 76 Russian combat units, known as battalion tactical groups, in eastern and southern Ukraine, up from 65 last week.

That could translate to around 50,000 to 60,000 troops, based on what the Pentagon said at the start of the war was the typical unit strength of 700 to 800 soldiers, but the numbers are difficult to pinpoint at this stage in the fighting.

The official also said that four US cargo flights arrived in Europe on Sunday with an initial delivery of weapons and other materials for Ukraine as part of a US$800 million package announced by Washington last week. And training of Ukrainian personnel on US 155 mm howitzers is set to begin in the next several days.

Ukraine halted civilian evacuations for a second day on Monday, saying Russian forces were shelling and blocking the humanitarian corridors.

Deputy Prime Minister Iryna Vereshchuk said Ukraine had been negotiating safe passage from cities and towns in eastern and southeastern Ukraine, including Mariupol and other areas in the Donbas. The government of the Luhansk region in the Donbas said four civilians trying to flee were shot and killed by Russian forces.

Vereshchuk warned Russia on social media: “Your refusal to open these humanitarian corridors will in the future be a reason to prosecute all involved for war crimes.”

The Russians, in turn, accused “neo-Nazi nationalists” in Mariupol of hampering the evacuation.

The capture of Mariupol, where Ukrainians estimate 21,000 people have been killed, is seen as key, and not just because it would deprive Ukraine of a vital port and complete a land bridge between Russia and the Crimean Peninsula, seized by Moscow eight years ago.

The US defence official said that if Russian forces succeed in taking full control of Mariupol, it could free up nearly a dozen battalion tactical groups for use elsewhere in the Donbas.

Meanwhile, a pro-Russian Ukrainian politician who was arrested last week on a treason charge appeared in a video offering himself in exchange for the evacuation of Mariupol’s trapped defenders and civilians. Ukraine’s state security services posted the video of Viktor Medvedchuk, the former leader of a pro-Russian opposition party with personal ties to Russian President Vladimir Putin.

It was not clear whether Medvedchuk was speaking under duress.

Putin repeated his insistence that the Western sanctions “blitz” against Russia has failed.

He said the West has not managed to “provoke panic in the markets, the collapse of the banking system and shortages in stores,” though he acknowledged a sharp increase in consumer prices in Russia, saying they rose 17.5 per cent.