Luhansk governor Serhiy Gaidai said Lysychansk was suffering "catastrophic" damage from shelling as Russian forces targeted the city following the fall of neighbouring Sievierodonetsk over the weekend.

He urged civilians to urgently evacuate Lysychansk.

Zelenskiy was due to make a video address on Monday to leaders of the Group of Seven (G7) advanced industrial nations who are meeting in Germany. Overnight, he stressed the urgency of the need for more arms, including a modern air defence system.

"Partners need to move faster if they are really partners, not observers. Delays with the weapons transfers to our state, any restrictions - this is actually an invitation for Russia to hit again and again," he said.

In Germany, US President Joe Biden told allies "we have to stay together" against Russia in the face of its assault on Ukraine, now in its fifth month.

The US is likely to announce this week the purchase of advanced medium to long range surface-to-air missile defence for Ukraine, a source familiar with the matter told Reuters.

The G7 summit is dominated by the war in Ukraine and its impact on food and energy supplies and the global economy.

At the meeting's start, four nations moved to ban imports of Russian gold to tighten the sanctions squeeze on Moscow and cut off its means of financing the invasion of Ukraine.

The General Staff of Ukraine's Armed Forces said on Monday Russian forces were using artillery to try to cut off Lysychansk from the south. Russian war planes had also struck near Lysychansk, the general staff said in its daily update.

Tass news agency on Sunday quoted an official from Moscow-backed separatists as saying Russian forces had entered Lysychansk from five directions and were isolating Ukrainian defenders.

"Lysychansk, it was a horror, the last week," said Elena, an elderly woman from the city who was among dozens of evacuees who arrived in the Ukrainian-held town of Pokrovsk by bus from frontline areas. "I already told my husband if I die, please bury me behind the house," she said.

In a big setback for Ukraine, Russian forces won full control of Sievierodonetsk, Lysychansk's twin city on the eastern bank of the Siversky Donets River, over the weekend when Ukrainian troops pulled out after weeks of intense bombardments and street fighting.

Luhansk and neighbouring Donetsk province make up Ukraine's eastern Donbas region - the country's industrial heartland.

The Donbas became a prime target for the Kremlin after Russian troops failed to take the capital Kyiv in the early stages of the war.

Russian forces also control a swathe of territory in the south, including the port city of Mariupol, which fell after weeks of siege warfare which left it in ruins.

Russian missiles also struck Kyiv for the first time in weeks on Sunday.

Missiles hit a bridge in the central city of Cherkasy linking western Ukraine and the eastern battlefields on Sunday, Ukrainian presidential adviser Oleksiy Arestovych said.

Odesa regional administration spokesperson Serhiy Bratchuk said a missile strike in the Odesa region, in southern Ukraine, had destroyed residential buildings and caused a fire. Six people were injured including a child, he added.

Western countries rallied around Kyiv when Russia invaded Ukraine in February, but more than four months into the war, that unity is being tested as soaring inflation and energy shortages rebound on their own citizens.

At the summit in Germany, US President Biden emphasised the need for unity amid concern that there were diverging opinions in European capitals about how to handle the situation.

"Putin has been counting on it from the beginning that somehow the NATO and the G7 would splinter. But we haven't and we're not going to," Biden said.

Australian Associated Press