Rockets strike Ukraine's Lviv

US President Joe Biden called Russian leader Vladimir Putin a butcher who "cannot remain in power" after meeting Ukrainian refugees in Poland, as Kremlin forces stepped up attacks across Ukraine, including the western city of Lviv.

Biden's comments, an escalation of US rhetoric towards Moscow over its invasion of Ukraine, were not a call for regime change in Russia, a White House official said, but meant to prepare the world's democracies for an extended conflict, reports Reuters.

Just before he spoke outside Warsaw's Royal Castle on Saturday, four missiles hit the outskirts of Lviv, just 60 km (40 miles) from the Polish border, local officials said.

Another strike significantly damaged Lviv's infrastructure but caused no reported deaths.

As the fight since Russia's Feb 24 invasion of its neighbour drags on, a visibly irritated Ukrainian President Volodymyr Zelenskiy again demanded Western nations send military hardware.

He asked whether they were intimidated by Moscow, saying, "We've already been waiting 31 days."

Biden, in a fiery speech ending a European trip aimed at bolstering Western resolve, framed the war as part of a historic struggle for democratic freedoms.

"For God's sake, this man cannot remain in power," Biden said as he ended his speech. The Kremlin dismissed the comment, saying: "That's not for Biden to decide. The president of Russia is elected by Russians."

Biden, after meeting refugees in Poland, called Putin a "butcher".

"We need to be clear-eyed. This battle will not be won in days or months," he said. "We need to steel ourselves for a long fight ahead."

Moscow says the goals for what Putin calls a "special military operation" include demilitarising and "denazifying" its neighbour. Ukraine and its Western allies calls this a pretext for an unprovoked invasion.