Russian forces bombarded areas of Ukraine's eastern Donbas region from land and air on Friday, destroying houses in residential districts and killing a number of civilians, Ukrainian officials said.
Ukraine’s President Volodymyr Zelensky said the assaults had turned the Donbas into "hell".
In the southern port city of Mariupol, the scene of the war's bloodiest siege, the last heavily wounded fighters from hold-out Ukrainian units had been evacuated from their bastion, the Azovstal steelworks, their commander said.
It was not clear if the remaining defenders there had definitively laid down their arms, reports Reuters.
The Kremlin meanwhile said it was bolstering its forces on Russia's western border, saying that moves by Finland and Sweden to join NATO were part of an increase in military threats.
As the war neared its three-month mark, the Ukrainian military said massive artillery barrages, including from multiple rocket launchers, had hit civilian infrastructure in the Donbas region bordering Russia.
Russian aircraft had also struck targets, the general staff said in a statement.
"The Russian army has started very intensive destruction of the town of Sievierodonetsk, the intensity of shelling doubled, they are shelling residential quarters, destroying house by house," Luhansk governor Serhiy Gaidai said via his Telegram channel.
"We do not know how many people died, because it is simply impossible to go through and look at every apartment," he said.
Earlier reports had put the civilian death toll in the Luhansk area of the Donbas at 13 in the past day, with 12 of them in Sievierodonetsk, which lies on a river about 110 km (70 miles) northwest of the regional capital.
"The Donbas is completely destroyed," President Zelensky said on Thursday night. "It is hell there - and that is not an exaggeration."
Reuters could not independently verify the reports and Russia denies targeting civilians.
In Moscow, Russian Defence Minister Sergei Shoigu said the "liberation of the Luhansk People's Republic" would be completed soon.
An industrial region, Donbas compromises the Donetsk and Luhansk areas, parts of which were already controlled by Moscow-backed separatists before the war. Shoigu said Russian troops and separatist militias were expanding their control there.
Russia's focus on the Donbas follows its failure to capture the capital Kyiv in the early stages of the invasion launched by Russian President Vladimir Putin on February 24.
In the weeks of warfare pitting Russia's military might against dogged Ukrainian resistance, thousands of people have been killed and whole urban areas shattered in the gravest crisis in Europe in decades.
Almost a third of Ukraine's people have fled their homes, including more than 6 million who have left the country, while others remain trapped in cities pulverised by Russian bombardments.
Analysts say that while Russian forces have advanced in Luhansk, they have made less progress in Donetsk. They have also been pushed back from the city of Kharkiv, north of the Donbas and close to the Russian border.
British military intelligence said on Friday Russia is likely to further reinforce its operations in the Donbas once it finally secures Mariupol - the scene of a weeks-long siege and Moscow's biggest success in a campaign of mixed fortunes.
Putin calls the invasion a "special military operation" to rid the country of fascists - an assertion Kyiv and its Western allies say is a baseless pretext for an unprovoked war.
In a sign of Russia's need to boost its war effort, the parliament in Moscow said it would consider a bill to allow Russians over 40 and foreigners over 30 to sign up for the military.
The past week has seen Russia all but secure victory in Mariupol, with the Kyiv government ordering the defenders of the Azovstal steelworks to stand down.
British military intelligence said as many as 1,700 soldiers were likely to have surrendered at the plant. Russian Defence Minister Shoigu put the number of those laying down their arms at about 2,000.
Ukrainian officials, who have tried to arrange a prisoner swap, have declined to comment on the number, saying it could endanger rescue efforts.
The commander of Ukraine's Azov Regiment said on Friday all civilians and wounded Ukrainian fighters had now been evacuated from Azovstal.
"The heavily wounded received the necessary assistance and they were evacuated, to be later exchanged and delivered to territory controlled by Ukraine," Commander Denys Prokopenko said in a video message.
The process of removing the dead was still underway.
"I hope that in the near future, relatives and Ukraine will be able to bury their soldiers with honour," Prokopenko said.
The International Committee of the Red Cross said it had registered hundreds of prisoners from Azovstal now held by Russia, but it has not given a precise number.
Western powers, who have strongly condemned Russia's actions and sought to isolate Moscow with an array of sanctions, were stepping up support for Ukraine.
The Group of Seven rich nations on Thursday agreed to provide Ukraine with $18.4 billion to make up revenues as the war wrecks its economy.
The US Senate approved nearly $40 billion in new aid, by far the largest US aid package to date.
The White House is also working to get advanced anti-ship missiles to Ukraine to help defeat Russia's naval blockade, which has largely stopped Ukraine's food exports.
US Secretary of State Antony Blinken accused Russia of using food as a weapon, holding "hostage" supplies for millions around the world. The war has caused global prices for grains, cooking oils, fuel and fertiliser to soar.
The European Union said it is looking into ways of using the frozen assets of Russian oligarchs to fund the reconstruction of Ukraine, while the United States has not ruled out possibly placing sanctions on countries that purchase Russian oil.