Lord Lebedev, who owns the newspaper alongside The Independent, used the publication’s front page on Monday to write an open letter to the Russian leader.
The Russian-born crossbench peer, who is a long-term friend of Prime Minister Boris Johnson, said: “I plead with you to use today’s negotiations to bring this terrible conflict in Ukraine to an end.”
In a statement published alongside a photograph of a paramedic performing CPR on a girl injured by shelling, Lord Lebedev said: “On this page are the final minutes of a six-year-old child fatally injured by shells that struck her Mariupol apartment block on Sunday.
“She is still wearing her pink jacket as medics fight to save her. But it is too late. Other children, and other families, are suffering similar fates across Ukraine.
“As a Russian citizen I plead with you to stop Russians killing their Ukrainian brothers and sisters.
“As a British citizen I ask you to save Europe from war. As a Russian patriot I plead that you prevent any more young Russian soldiers from dying needlessly. As a citizen of the world I ask you to save the world from annihilation.”
He added that he hoped negotiations at the Ukraine-Belarus border “provide a moment of hope” and urged Mr Putin to end the war.
On Friday, the day after Russia launched its invasion into Ukraine, Lord Lebedev, who is the son of former KGB operative Alexander Lebedev, described the attack as an “unimaginable tragedy”.
“Orthodox Slavs killing their brethren on a scale not witnessed for centuries. An unimaginable tragedy for people of Ukraine and Russia,” he tweeted.
Other recent front pages of the newspaper have featured images of Ukrainians with bloodied faces and others devastated by the destruction of their homes.