Ukraine's military warned the public on Tuesday of more indiscriminate Russian shelling of critical infrastructure as US President Joe Biden issued one of his strongest warnings yet that Russia is considering using chemical weapons.

Russian troops have failed to capture any major Ukrainian city more than four weeks into their invasion, and increasingly are resorting to massive destruction of residential areas with airstrikes, long-range missiles and artillery.

The southern port of Mariupol has become a focal point of Russia's assault and is largely in ruins with bodies on the streets but attacks were also reported to have intensified on the second city of Kharkiv on Monday.

Russian forces were expected to...