Dmitry Medvedev said a slide in relations between his country and Nato is as bad as the height of the nuclear struggle with the Soviet Union.
Mr Medvedev raised the spectre of nuclear armageddon and referenced the Cuban Missile Crisis in an ominous speech to a world security conference.
He told participants in Munich that moves to beef up Nato forces in Eastern Europe show the West is hostile towards Russia.
British, US and other Western powers have deployed military assets to the region to reassure European nations.
Both Russia and Nato have carried out public troop manoeuvres in an escalation of tensions sparked by Ukraine.
Soldiers and vehicles patrolled areas at the fringes of Europe amid fears Russia would repeat its annexation of the Crimea with other ex-Soviet nations.
Just this week the UK dedicated five more warships to patrolling the Baltic, prompting more backlash from the Kremlin.
Speaking to the conference in Munich, Germany, Mr Medvedev said: "NATO's policies related to Russia remain unfriendly and opaque - one could go so far as to say we have slid back to a new Cold War."
"NATO continues to insist Russia constitutes its main threat — a threat to Europe as well as the US and other countries.
"Scary movies have been filmed where Russians begin a nuclear war. Sometimes I think: are we in 2016 or in 1962?"
The year 1962 marked the high point of nuclear brinkmanship in the Cold War.
In the autumn of that year, Russia tried to dispatch nuclear warheads to Cuba - just off the US border - but turned back after an intense showdown with US President John F Kennedy.
It is widely thought to be the closest the world has ever come to all-out nuclear war, Express reported.
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