The British PM made the statement regarding Vladimir Putin’s "cynical and barbaric" government in a Sky News interview.
He said: "The stuff that you’re hearing about chemical weapons is straight out of [the Russian] playbook.
"They start saying that there are chemical weapons stored by their opponents, or by Americans. So when they, themselves, deploy chemical weapons — as I fear they may — they have a fake story ready to go.
"And you’ve seen it in Syria, you saw it even in the UK ... I just note that that is what they’re already doing."
Two million people have fled Kyiv — around half the capital city’s total population, according to its mayor Vitali Klitschko said.
Despite the mass exodus, he insisted that Kyiv was still safe — saying: "[It] has been transformed into a fortress. Every street, every building, every checkpoint has been fortified."
Russian troops have failed to capture Kyiv since Putin launched the invasion on 24 February.
Our Russian conscripts are going on sick call. Some appear to be dying from unknown causes. Russia suspects Ukrainian BIO lab leaks. Russia and Chinese HAZMAT teams deployed. Russian conscripts ordered to report to 40 miles long convoy to pick up protective gear and test kits.