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.