The Prime Minister told the despot the "quickest way to end this conflict" is to withdraw his troops from Europe's biggest land war since 1945.
Western allies - including Britain are under intense pressure to allow Ukraine to use long-range missiles to strike targets deep inside Russia after the US made that move.
Moscow marked 1,000 days since its invasion by updating its weapons doctrine so any large conventional attack on the Russian capital could meet the criteria for a nuclear response.
Sir Keir, asked if Britons needed to prepare for nuclear war, said: "There's irresponsible rhetoric coming from Russia. That is not going to deter our support for Ukraine.
"We're now on day 1,000 of conflict, a thousand days of Russian aggression, a thousand days of sacrifice in Ukraine.
"We have stood with Ukraine from the start. I've been doubling down on my message that we should give Ukraine what it needs for as long as needed to win this war against Putin."
Sir Keir insisted the quickest way to end the conflict was for "Russia to cease", adding it was the "most simple and just way to do this".
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