Scores of Ukrainian civilians including women and children were trapped today in underground bunkers at a steelworks in the ruined port city of Mariupol.
Earlier, Russian President Vladimir Putin said Russia was ready to allow them to leave safely.
He told Israeli Prime Minister Naftali Bennett in a phone call that Kyiv should order Ukrainian fighters defending the besieged Azovstal plant to disarm, and Russia was still prepared to provide safe passage out for civilians.
Ukrainian defenders at the site have clung on desperately for weeks.
Captain Sviatoslav Palamar, a deputy commander of Ukraine's Azov Regiment, posted a video online which purported to be shot in Mariupol's Azovstal steel works and said "heavy, bloody fighting is going on."
The Kremlin denied a Ukrainian claim that its forces were storming the plant and said humanitarian corridors were currently operating there.
More than 300 civilians have been evacuated from Mariupol and other areas in southern Ukraine as part of a joint UN-Red Cross operation, the United Nations said.
Mariupol is an important target in Russian efforts to cut Ukraine off from its coastal grain and metals export routes, as well as to link Russian-controlled territory in the east of the country to Crimea, seized by Moscow in 2014.
"God forbid more shells hit near the bunkers where the civilians are," said Tetyana Trotsak, an Azovstal evacuee among dozens who reached a Ukraine-controlled town this week.
Russia said its artillery struck multiple Ukrainian positions and strongholds overnight, killing 600 fighters. Reuters could not independently verify the claim.
Ukrainian authorities reported shelling of towns near afrontline that divides territory it holds in the Donetsk and Luhansk regions from land held by Russian-backed separatists.
The Ukrainian air force said it had downed three Russian cruise missiles and four aircraft, including two Sukhoi fighter jets.
A Ukrainian presidential adviser said he did not expect Russia's offensive to produce "significant results" before it holds the annual May 9 Victory Day in Moscow to mark the anniversary of the Soviet Union's triumph over Nazi Germany.
The Kremlin said the United States and other NATO countries were "constantly" feeding intelligence to Ukraine but this would not stop Russia achieving its military goals there.
It comes as a top EU diplomat said European Union countries are "almost there" in agreeing the bloc's proposed new package of sanctions against Russia, including an oil embargo.
Foreign policy chief Josep Borrell said: "I hope that they will get an agreement. They are almost there.
"And we need this agreement because we have to push still more our economic and financial pressure on Russia." Oil prices jumped on the proposed EU ban.
US President Joe Biden said he would speak with leaders from the G7 advanced economies this week about more sanctions.
The British government said it had sanctioned steel manufacturing and mining company Evraz, whose biggest shareholder is sanctioned billionaire Roman Abramovich.
Russia calls its actions a "special military operation" to disarm Ukraine and protect it from fascists. Ukraine and the West say the fascist allegation is baseless and that the war is an unprovoked act of aggression.
More than five million Ukrainians have fled abroad since the start of the invasion.
