The British Defense Ministry said that British jets were also involved, but did not have immediate details.
Lt. Col. John Inge Oeglaend, of the Norwegian Joint Headquarters, said the bombers, all Tupolev-95s, neared but did not enter Norwegian air space in the far north.
"They followed a normal route in international air space," he said by telephone from the western Norway port of Stavanger. He said they flew near Norway's northern tip over the Barents Sea, then over the North Atlantic and back.
Oeglaend said two Norwegian fighters were sent up both times that the Russian aircraft approached Norway, in keeping with normal practice.
Norway, a member of the NATO alliance, and Russia shared land and ocean borders in the Arctic, including the vast Barents Sea.
According to Oeglaend, this is the third time Norwegian fighters have scrambled since mid-July to monitor a rising number of Russia military air exercises.