Dr. Holdren said in an interview that administration officials were trying “to get our arms around matching the resources and the commitment we can bring to bear with the magnitude of the opportunities and the challenges” in the Arctic.

What kind of frontier the Arctic will be — an ecological preserve or an economic engine, an area of international cooperation or confrontation — is now the question at the center of the unfolding geopolitical competition. An increasing divergence over the answer has deeply divided the United States and its allies on one side and Russia on the other.

Since returning to the Kremlin for a third term in 2012, President Vladimir V. Putin has sought to restore Russia’s pre-eminence in its northern reaches — economically and militarily — with zeal that a new report by the Center for Strategic and International Studies compared to the Soviet Union’s efforts to establish a “Red Arctic” in the 1930s. The report’s title echoed the rising tensions caused by Russia’s actions in the Arctic: “The New Ice Curtain.”

Decades of cooperation in the Arctic Council, which includes Russia, the United States and six other Arctic states, all but ended with Moscow’s annexation of Crimea in 2014 and the continuing war in eastern Ukraine. In March, Russia conducted an unannounced military exercise that was one of the largest ever in the far north. It involved 45,000 troops, as well as dozens of ships and submarines, including those in its strategic nuclear arsenal, from the Northern Fleet, based in Murmansk.

The first of two new army brigades — each expected to grow to more than 3,600 soldiers — deployed to a military base only 30 miles from the Finnish border. The other will be deployed on the Yamal Peninsula, where many of Russia’s new investments in energy resources on shore are. Mr. Putin has pursued the buildup as if a 2013 protest by Greenpeace International at the site of Russia’s first offshore oil platform above the Arctic Circle was the vanguard of a more ominous invader.

“Oil and gas production facilities, loading terminals and pipelines should be reliably protected from terrorists and other potential threats,” Mr. Putin said when detailing the military buildup last year. “Nothing can be treated as trivial here.”

In Washington and other NATO capitals, Russia’s military moves are seen as provocative — and potentially destabilizing.