It comes amid concerns that with Russia struggling to make ground in Ukraine, Putin could turn to nuclear weapons.
“We’ve never said anything proactively about possible use of nuclear weapons by Russia. We have only hinted in response to those statements that the Western leaders have made,” he said, according to a live translation on Sky News.
Referring to the former prime minister, he said: “Liz Truss, the ex-prime minister of the United Kingdom, she said it directly.
“In her conversation with a representative of the media, she said that the UK is a nuclear power and the prime minister has, in their mandate, the possible use of nuclear weapons.
“I’m not quoting her and she said that she’s prepared to do that.
“And no-one responded in any way.
“Well, she just made a folly, she was a bit out of it.
“But can you say these things publicly? Well, even if she said it, someone should have corrected that.
“Washington, for example, could have said that they have nothing to do with that.”
It was not immediately clear what comments Putin was referring to, but during the Tory leadership contest over the summer Ms Truss had been asked about the potential use of nuclear weapons.
During a hustings in August, she was asked how she would feel about having to make decisions about nuclear warfare, she said: “I think it is an important duty of the prime minister, I am ready to do that.”
Foreign Secretary James Cleverly hit out at Putin after the Russian president delivered his latest speech.
“Putin’s message today to the Russian people is unclear, untrue and unedifying,” he tweeted.
“What is crystal clear, is our message to the world:
“Aggressors must not be able to invade their neighbours with impunity.
“We will resolutely support Ukraine in its fight for freedom and democracy.”