Based in Severomorsk in the Barents Sea in the Arctic, the carrier Admiral Kuznetsov and seven other vessels were photographed on Monday in international waters off Norway, Major Elisabeth Eikeland, spokeswoman of the National Joint Headquarters in the Norwegian army, told AFP.
"We have been informed that they are en route to the Mediterranean," Eikeland said.
"It's not every day that so many ships sail together off Norway," she said.
The carrier was shadowed by a Norwegian navy frigate, with a vessel from another NATO member primed to take over escort duties afterwards, Eikeland said.
"The tone is good" with the Russian ships, Eikeland said.
Russia announced on Saturday that the Soviet-era Admiral Kuznetsov, its only aircraft carrier, was to reinforce Moscow's military presence in the eastern Mediterranean, where its forces are conducting a bombing campaign in Syria.
The Admiral Kuznetsov is travelling with the Pyotr Veliky battlecruiser, the Vice Admiral Kulakov destroyer and large anti-submarine ships, the defence ministry in Moscow said.
On Tuesday, Moscow announced an immediate halt to raids by Russian and Syrian air forces on Aleppo as a gesture of "goodwill".
The Kremlin said this would enable the evacuation of civilians from rebel-held areas of the city, which has been bombed intensively during the past month.