"NATO has no intention of increasing its presence and activities in the Far North," Fogh Rasmussen said in Oslo after spending two days visiting northern Norway.
The Arctic is believed to hold some 90 billion barrels of oil and 30 percent of the world's yet-to-be discovered natural gas resources.
Those riches have become increasingly accessible as the Arctic ice shrinks. Not only countries bordering the Arctic Ocean are keen to claim the resources but also other nations further afield, such as China, are looking on with interest.
Several states, including Russia, Canada and the United States, have already announced a reinforcement of their military presence to defend their claims.
Norway, which shares a border with Russia, has made the Far North its top priority and has in recent years tried to draw the attention of NATO and the European Union to the region.
"Norway has, like all other allies, a legitimate expectation that NATO's collective defence should cover all of NATO's territory, including of course the north of Norway," Fogh Rasmussen said at a joint press conference with Prime Minister Jens Stoltenberg.
"The Arctic is a hard environment. It rewards cooperation, not confrontation. I trust we'll continue to see cooperation," the NATO chief wrote on Tuesday evening on Twitter.
The foreign ministers of the Arctic Council, an international forum for the eight states bordering the Arctic, are to meet on May 15th in Kiruna, in northern Sweden.
Among other things, they are to consider a request from several other nations and bodies - China, India, Italy, Japan, Singapore, South Korea, and the EU - to be granted observer status on the Council.
Britain, France and Germany are among those who already hold observer status.