Destroyed cars are seen at the site of a shopping center after it was hit in a military strike in Kyiv, Ukraine. Reuters

Ukraine's military said on Tuesday residents should brace for more indiscriminate Russian shelling of critical infrastructure, as US President Joe Biden issued one of his strongest warnings yet that Moscow is considering using chemical weapons.

Biden said Monday that it's "clear" Russia is considering the use of chemical and biological weapons in Ukraine and warned of a "severe" Western response if it chose to do so.

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"His back is against the wall," said Biden of Russian President Vladimir Putin, noting that Russia has recently accused the United States of holding chemical and biological weapons in Europe.

US President Joe Biden gestures during a meeting. File photo

"Simply not true. I guarantee you," he told a gathering of US business leaders in Washington.

"They are also suggesting that Ukraine has biological and chemical weapons in Ukraine. That's a clear sign he's considering using both of those," he said.

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

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

Russian President Vladimir Putin speaks during a press conference. File photo

Without citing evidence, Biden said Russia's false accusations that Kyiv had biological and chemical weapons illustrated that President Vladimir Putin was considering using them himself.

Putin's "back is against the wall and now he's talking about new false flags he's setting up including, asserting that we in America have biological as well as chemical weapons in Europe, simply not true," Biden said at a Business Roundtable event.

"They are also suggesting that Ukraine has biological and chemical weapons in Ukraine. That's a clear sign he's considering using both of those."

The Russian embassy in Washington did not immediately respond to a request for comment.