The former world heavyweight boxing champion was attending the funeral of a well-known 24-year-old anti-corruption activist when the remarks were made.
Volunteer soldier Roman Ratushny was killed in Izyum, in the Kharkiv region, on 9 June.
Mayor Klitschko, who won legions of fans across the world during his long record-breaking career, said the Russian leader was destroying millions of lives in both Ukraine and his own country.
“This is also a tragedy for Russians and for the Russian Federation. The people do not understand that right now, but I am sure they will realise very soon the reality. The Russians die – for what? The ambition of Putin?”
The mayor was among hundreds of mourners who turned out to pay their respects to Mr Ratushny – who came to prominence during pro-democracy protests in 2013 against the pro-Moscow former Ukrainian government.
His coffin was carried into Independence Square, where friends gave tributes and dozens of mourners stepped forward to leave bouquets of flowers.
Vitali Klitschko said Western allies showing solidarity with Ukraine was “key for peace and freedom in Europe.”
Mr Johnson said allies needed to demonstrate they were giving Ukraine “strategic resilience”.
The prime minister’s visit came just a day after the leaders of France, Germany, Italy and Romania all arrived in Ukraine to give their support to the country’s ambitions to join the EU.
When I asked Mayor Klitschko if he was concerned Ukraine could be pressured to make concessions to the Russians, he said ceding Ukrainian land should not happen.
“I’m more than sure we will be ready to talk with the Russians about some compromise. If the last Russian soldier left Ukraine, it will be time to talk but not yet. Russians have to go from our homeland.”
As one of the most recognisable Ukrainians in the world, Mayor Klitschko’s voice carries weight. But the ultimate decision on if and when to enter peace talks will be down to President Zelensky and his government.
