Dmitry Medvedev spoke at the Munich Security Conference shortly before John Kerry, the US Secretary of State, accused Russia of “repeated aggression” and killing civilians.
The country has come under heavy criticism for its intervention in Syria, where it is predominantly believed to be targeting anti-government rebels in support of Bashar al-Assad, and is under international sanctions for its annexation of Crimea.
Jens Stoltenberg, the Nato Secretary General, added to the pressure today by telling senior diplomats, politicians and defence officials a “more assertive” Russia was “destabilising the European security order”.
“Nato does not seek confrontation - we do not want a new Cold War,” he said.
“At the same time our response has to be firm.”
But Mr Medvedev responded strongly, blaming Nato itself for worsening tensions with a new missile system based in Romania and increased presence along the Russian border.
“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,” he said.
Scoffing at what he said was a suggestion that Moscow may use nuclear weapons in a first strike, he quipped: “Sometimes I wonder if it's 2016 or if we live in 1962.”
The Russian Prime Minister called for sanctions on Russia implemented after it annexed Crimea from Ukraine in March 2014 to be lifted, saying they were “a road that leads nowhere”.
“The longer the sanctions continue, chances for the Europeans to keep their position at the Russian market as investors and suppliers are fading,” he added.
“That's why one has to act quickly.”
Mr Medvedev also defended his country’s intervention in Syria, saying it is targeting Isis and has been open with its goals.
A war of words has been raging between American and Russian defence officials over the bombing of hospitals and civilian areas in Aleppo, where regime forces are pushing to take territory from anti-government rebels.
Russia has insisted it is targeting Isis but the UN and monitoring groups claim data shows its air strikes have predominantly hit “moderate” rebels, who are styled as “terrorists” by Assad but viewed by the West as a legitimate and effective fighting force against Isis and other extremists.
Mr Kerry said Russia was defying the international community with its support for the Assad regime and separatists in eastern Ukraine.
In pictures: Russian air strikes in Syria
In pictures: Russian air strikes in Syria
Volunteers from Syria Civil Defence, also known as the White Helmets, help civilians after Russia carried out its first airstrikes in Syria
The aftermath of Russian airstrike in Talbiseh, Syria
Smoke billows from buildings in Talbiseh, in Homs province, western Syria, after airstrikes by Russian warplanes
Russian Air Forces carry out an air strike in the ISIS controlled Al-Raqqah Governorate. Russia's KAB-500s bombs completely destroy the Liwa al-Haqq command unit
Caspian Flotilla of the Russian Navy firing Kalibr cruise missiles against remote Isis targets in Syria
Caspian Flotilla of the Russian Navy firing Kalibr cruise missiles against remote Isis targets in Syria, a thousand kilometres away. The targets include ammunition factories, ammunition and fuel depots, command centres, and training camps
Russia claimed it hit eight Isis targets, including a "terrorist HQ and co-ordination centre" that was completely destroyed
A release from the Russian defence ministry purportedly showing targets in Syria being hit
A video grab taken from the footage made available on the Russian Defence Ministry's official website, purporting to show an airstrike in Syria
Russia launched air strikes in war-torn Syria, its first military engagement outside the former Soviet Union since the occupation of Afghanistan in 1979. Russian warplanes carried out strikes in three Syrian provinces along with regime aircraft as Putin seeks to steal US President Barack Obama's thunder by pushing a rival plan to defeat Isis militants in Syria
“To date, the vast majority of Russia's attacks (in Syria) have been against legitimate opposition groups,” he said.
“To adhere to the agreement it made, Russia's targeting must change.”
He also said US sanctions would hold until Russia helps implement the Minsk agreement drawn up with the aim of ending the Ukrainian conflict.
A temporary “cessation of hostilities” in Syria was agreed in Munich in the early hours of Friday but hopes for a long-lasting truce are waning with Assad’s vow to retake the whole of Syria by force, and Saudi Arabia’s deployment of troops and planes in Turkey ahead of an expected intervention.
Additional reporting by agencies