Rockets struck the western Ukrainian city of Lviv on Saturday, signalling a potential new front in Moscow's invasion as US President Joe Biden decried Russian President Vladimir Putin's power and sought to steel Europe for a long fight ahead.

Intense fighting raged in several parts of Ukraine, suggesting there will be no swift let-up in the month-old war while Biden framed the fight as part of the historic struggle for democratic freedoms in a major address from Poland as he concluded his European trip aimed at bolstering Western resolve.