The Russian leader said on Sunday he was putting Moscow's nuclear forces on a "special regime of combat duty" in response to "aggressive statements" coming from Western powers.
But Johnson suggested Putin's actions were more to do with the fact his forces were meeting with "more resistance than the Kremlin had bargained for".
He also cast doubt on possible negotiations between Russian and Ukrainian delegations to try to resolve the crisis.
Ukraine President Volodymyr Zelenskiy agreed the two sides could meet on the Ukraine-Belarus border having initially rejected an offer of talks in Belarus.
However Johnson said he had seen nothing to suggest Putin was genuine in his offer.
"There's nothing I've seen so far in his behaviour that leads me to think that he could possibly be sincere," the British PM said.
Earlier, Russian television footage showed Putin meeting with his defence minister and the chief of the general staff, and instructing them to ready the nation's nuclear forces.
"Western countries aren't only taking unfriendly actions against our country in the economic sphere, but top officials from leading NATO members made aggressive statements regarding our country," he said.
But on a day when the expected assault on Kyiv again failed to materialise and the Ukrainians claimed to have driven Russian forces out of the country's second city Kharkiv, Mr Johnson said Putin's words were "a distraction from the reality of what's going on".
"This is an innocent people who are facing a totally unprovoked act of aggression against them, and what's actually happening is that they are fighting back perhaps with more effect, with more resistance, than the Kremlin had bargained for," he said.
"You can see some of the logistical difficulties that the Russian forces are experiencing.
"The Russian defence ministry have themselves conceded that they're having casualties.
"This is a disastrous misbegotten venture by President Putin."
