The Russian President is seeking to turn Russia into a “major power” once again, General Sir Mike Jackson said.
The warning comes after Theresa May accused Moscow of planting fake stories” to “sow discord in the West”.
Addressing business leaders in London, the Prime Minister said Russia could be a valuable partner of the West but only it if “plays by the rules”.
Mrs May added: “Russia has repeatedly violated the national airspace of several European countries and mounted a sustained campaign of cyber espionage and disruption.
“This has included meddling in elections and hacking the Danish Ministry of Defence and the Bundestag among many others.
“We know what you are doing and you will not succeed. Because you underestimate the resilience of our democracies, the enduring attraction of free and open societies and the commitment of Western nations to the alliances that bind us.”
Sir Mike told LBC that the alleged meddling forms part of President Putin’s plans to return to rebuild the Soviet Union.
He said: “I always like to remind people regarding Vladimir Putin that he said publicly… That the worst thing, the worst thing let me underline that, that happened in the 20th century, worse than two world wars, worse than the Holocaust, worse than the Great Depression – the worst thing was the fall of the Soviet Union.
“It tells you quite a lot, I think, about Putin because he sees modern Russia as the inheritor of the great power status which the Soviet Union used to have and I think he’s trying to rebuild that.”
He added: “It’s a theme which is there, to rebuild modern Russia as a major power in the world as the Soviet Union was in his view.”
Sir Mike was seemingly referencing an address Vladimir Putin delivered in 2005 to Russia’s top politicians.
President Putin said: “Above all, we should acknowledge that the collapse of the Soviet Union was a major geopolitical disaster of the century.
“As for the Russian nation, it became a genuine drama. Tens of millions of our co-citizens and co-patriots found themselves outside Russian territory. Moreover, the epidemic of disintegration infected Russia itself.”