Russia on Thursday made an all-out effort to capture the rest of the industrial region of Lugansk in eastern Ukraine, officials said, as President Volodymyr Zelensky accused Moscow of seeking to commit "genocide" across the eastern Donbas.

As the fighting intensified, Foreign Minister Dmytro Kuleba aired Kyiv's increasing frustration with the West, accusing allies of dragging their feet on arms deliveries and telling his German counterpart that Ukraine needs heavy weapons "as soon as possible."

Russian forces are now closing in on several urban centres, including the strategically located Severodonetsk and Lysychansk. Lugansk is part of the Donbas, the industrial basin comprising that region and Donetsk.

"The situation remains difficult, because the Russian army has thrown all its forces at taking the Lugansk region," regional governor Sergiy Gaiday said in a video on Telegram.

"Extremely fierce fighting is taking place on the outskirts of Severodonetsk. They are simply destroying the city, they are shelling it every day, shelling without pause."

Russian forces also bombarded Ukraine's second city Kharkiv, killing nine people, and five civilians were killed Thursday in the Donetsk region to the south, according to the governor.

In his daily televised address, Zelensky said Moscow was pursuing an "obvious policy of genocide" in the Donbas -- after failing to take the capital Kyiv -- and its bombardments could leave the entire region "uninhabited".

Kyiv has been losing patience with what it views as the West's failure to quickly arm Ukraine and impose a ban on Russian oil exports on top of punishing economic sanctions already in place.

"We need more heavy weapons delivered as soon as possible, especially MLRS (multiple launch rocket systems) to repel Russian attacks," Kuleba wrote on Twitter after speaking with Germany's Annalena Baerbock.

'Maximum intensity'

Earlier in the day, Ukrainian Deputy Defence Minister Ganna Malyar told journalists that fighting in the east had reached "its maximum intensity" since Russia invaded its neighbor on February 24.

Pro-Moscow separatist groups have since 2014 controlled parts of Donbas, but Russia now appears set on taking the whole region.

"Enemy forces are storming the positions of our troops simultaneously in several directions. We have an extremely difficult and long stage of fighting ahead of us," Malyar said.

Gaiday said three people died in recent Russian attacks on Severodonetsk and Lysychansk, which stand on the crucial route to Ukraine's eastern administrative centre in Kramatorsk.

In Kramatorsk itself, children roamed the rubble left by Russian attacks as the sound of artillery fire boomed.

"I got used to the shelling," said Yevgen, a sombre-looking 13-year-old who moved to Kramatorsk with his mother from the ruins of his village Galyna.

And fresh shelling around Kharkiv killed another nine people and injured 19, officials said.

"Today the enemy insidiously fired on Kharkiv," regional governor Oleg Sinegubov said on social media, warning residents to evacuate to air raid shelters.

An AFP reporter in Kharkiv saw plumes of smoke rising from the stricken area, along with several people injured near a shuttered shopping centre. An elderly man with injuries to his arm and leg was carried away by medics.

'Show me one Nazi!'

Russia's rationale of a "special military operation" to "demilitarize and de-Nazify" Ukraine drew a snort of derision in one village near Kharkiv that came under fire.

"Show me one Nazi in the village! We have our nation, we are nationalists but not Nazis nor fascists," said retired nurse Larysa Kosynets.

Elsewhere, in the strategic southern port city of Mariupol, occupying authorities cancelled school holidays to prepare students to switching to a Russian curriculum, said a Ukrainian official.

Mariupol fell to Russia earlier this month after a devastating siege that left thousands dead the reduced the city to rubble.

"Throughout the summer, children will have to study Russian language, literature and history as well as math classes in Russian," city official Petro Andryushchenko wrote on social media.

'Trust is lost for generations'

Finnish Prime Minister Sanna Marin on Thursday became the latest Western official to visit Kyiv, where she said it would take Russia decades to repair its standing in the world after invading Ukraine.

"Trust is lost for generations," Marin told a press conference.

German Chancellor Olaf Scholz, who has faced criticism over Berlin's slow response, also weighed in Thursday, saying Russian President Vladimir Putin will not negotiate seriously until he realizes he might not win in Ukraine.

"Our goal is crystal-clear -- Putin must not win this war. And I am convinced that he will not win it," Scholz told the World Economic Forum in Davos.

Food crisis fears

The Ukraine conflict has sparked fears of a global food crisis, on top of the political and economic shockwaves that have already reverberated around the world.

The Kremlin on Thursday pointed the finger at Western countries for stopping grain-carrying vessels from leaving ports in Ukraine -- rejecting accusations that Russia was to blame.

Putin said Moscow was ready to make a "significant contribution" to averting the crisis if the West lifts sanctions imposed on Russia over Ukraine, in a telephone call with Italy's Prime Minister Mario Draghi.

Speaking to journalists after the call, Draghi said he would continue talking to both Moscow and Kyiv to resolve the food crisis, but added that he had little optimism for ending the war.

"When asked if I have seen any glimmer of hope for peace, the answer is no," the Italian prime minister said.