Russian forces have pushed forward in their assault on Ukraine, seeking to capture the crucial southern port city of Mariupol as Moscow prepared to celebrate its national Victory Day holiday.

Determined to show a success in a war now in its 11th week, Russian troops have targeted a sprawling seaside steel mill where an estimated 2,000 Ukrainian fighters were making what appeared to be their last stand to save Mariupol from falling.

The mill is the only part of the city not overtaken by the invaders, and its defeat would deprive Ukraine of a vital port and allow Russia to establish a land corridor to the Crimean Peninsula, which it seized from Ukraine in 2014.

Ukrainian President Volodymyr Zelensky has warned that worsening attacks could be linked to Victory Day, which marks Russia’s greatest triumph, over Nazi Germany in 1945. Russian President Vladimir Putin may want to proclaim a win in Ukraine when he addresses troops parading on Red Square.

Though fighting continues on multiple fronts, Russia is closest to victory in Mariupol.

Ukrainian fighters in the steel mill have rejected deadlines set by the Russians for laying down their arms even as attacks continued by warplanes, artillery and tanks.

The last of the civilians taking shelter with fighters at the plant were evacuated on Saturday. They arrived on Sunday night in Zaporizhzhia, the first major Ukrainian city beyond the frontlines, and spoke of constant shelling, dwindling food, ubiquitous mould — and using hand sanitizer for cooking fuel.

Elsewhere in Ukraine, more than 60 people were feared dead after a Russian bomb flattened a school being used as a shelter in the eastern village of Bilohorivka, Ukrainian officials said.

Authorities said about 90 people were sheltering in the school’s basement when it was attacked on Saturday. Emergency crews found two bodies and rescued 30 people, but “most likely all 60 people who remain under the rubble are now dead”, Serhiy Haidai, governor of Luhansk province, wrote on the Telegram messaging app.

Russian shelling also killed two boys, aged 11 and 14, in the nearby town of Pryvillia, Haidai said. Luhansk is part of the Donbas, the industrial heartland in the east that Russia’s forces are working to capture.

On Ukraine’s coast, explosions echoed again across the major Black Sea port of Odesa. The Ukrainian military said Moscow was focusing its main efforts on destroying airfield infrastructure in eastern and southern Ukraine.

In a sign of the dogged resistance that has sustained the fighting into its 11th week, Ukraine’s military struck Russian positions on a Black Sea island that was captured in the war’s first days. A satellite image by Planet Labs showed smoke rising from two sites on the island.

But Moscow’s forces showed no sign of backing down in the south. Satellite photos show Russia has put armoured vehicles and missile systems at a small base in the Crimean Peninsula.

The most intense combat in recent days has taken place in eastern Ukraine. A Ukrainian counteroffensive in the northeast near Kharkiv, the country’s second-largest city, is making “significant progress”, according to the Institute for the Study of War, a Washington think tank.

However, the Ukrainian army withdrew from the embattled eastern city of Popasna, regional authorities said.

Rodion Miroshnik, a representative of the pro-Kremlin, separatist Luhansk People’s Republic, said its forces and Russian troops had captured most of Popasna after two months of fierce fighting.

The Kharkiv regional administration said three people were killed in shelling of the town of Bogodukhiv, about 50 kilometres (30 miles) from Kharkiv.

South of Kharkiv, in Dnipropetrovsk province, the governor said a 12-year-old boy was killed by a cluster munition that he found after a Russian attack. An international treaty bans the use of such explosives, but neither Russia nor Ukraine has signed the agreement.

“This war is treacherous,” the governor, Valentyn Reznichenko, wrote on social media. “It is near, even when it is invisible.”

As Victory Day neared and the spotlight turned to Mr Putin, Western leaders showed new signs of support for Ukraine.

The Group of Seven industrial democracies pledged to ban or phase out imports of Russian oil.

The US also announced new sanctions against Russia, cutting off Western advertising from Russia’s three biggest TV stations, banning US accounting and consulting firms from providing services, and cutting off Russia’s industrial sector from wood products, industrial engines, boilers and bulldozers.

US first lady Jill Biden met with her Ukrainian counterpart. Canadian Prime Minister Justin Trudeau raised his country’s flag at its embassy in Kyiv. And U2′s Bono, alongside bandmate The Edge, performed in a Kyiv subway station that had been used as a bomb shelter, singing the 1960s song Stand by Me.

Mr Zelensky released a video address marking the day of the Allied victory in Europe 77 years ago, drawing parallels between Russia’s invasion of Ukraine and the evils of Nazism. The black-and-white footage showed Mr Zelensky standing in front of a ruined apartment block in Borodyanka, a Kyiv suburb.

He said that generations of Ukrainians understood the significance of the words “never again”, a phrase often used as a vow not to allow a repeat of the horrors of the Holocaust.