Defence Minister Sergei Shoigu, who is overseeing an expensive modernisation of the armed forces, said Russia faced new threats to its security which obliged it to boost its military strength and capabilities.
"New challenges and threats to military security require the armed forces to further boost their military capabilities. Special attention must be paid to strategic formations in the North," RIA quoted Shoigu as saying.
Russian Deputy Foreign Minister Aleksey Meshkov said on Monday, according to Tass news service, that Russia was "deeply concerned about the increase in exercises of NATO countries close to our borders".
It was "particularly surprising that this takes place in the north-eastern region of Europe, which is the most stable in security terms, not only on our continent but possibly in the world," Mr Meshkov said.
Tensions between Russia and the West have reached their worst level since the Cold War over the crisis in Ukraine.
The West and Kiev accuse Russia of supplying arms and soldiers to support pro-Russian separatists in eastern Ukraine who are fighting government troops.
NATO made new allegations last week that Russia was arming the separatists in east Ukraine, where more than 6000 people have been killed in nearly a year of fighting.
Moscow has boosted its ambitions in the resource-rich Arctic region, where it shares a border with NATO member Norway, and the military is looking to boost its capabilities in the region.
The exercises were due to include nearly 40,000 servicemen, 41 warships and 15 submarines, RIA reported.
Taking place over six days to March 21, the exercises would check the military's ability to strengthen forces on the islands of Novaya Zemlya and Franz Josef Land, defend Russia's borders by land and air, including in the country's far north, and destroy the naval grouping of a simulating enemy, Mr Shoigu said, according to Interfax.
The exercises began a day after Putin disclosed in a Russian television documentary that he was ready to put nuclear forces on alert when he annexed Ukraine's Crimea peninsula a year ago.
The almost year-long conflict that erupted between pro-Russian separatists and government troops has killed more than 6000 people in eastern Ukraine.
A ceasefire negotiated by the leaders of Ukraine, Russia, Germany and France in Minsk, Belarus, on February 12 is gradually taking hold.