NATO member Norway has said it will ask Washington to send 700 US Marines to its northern region, compared to 330 on "rotation" since early last year.
Oslo's announcement followed a call on Friday by nine nations along NATO's eastern flank, including Estonia, Poland and Romania, for a stronger alliance presence.
NATO has bolstered its defenses in Central and Eastern Europe in response to growing fears, following Moscow's annexation of Crimea in 2014.
Oslo's request coincided Tuesday with its filing of a legal challenge to the US tariffs on steel and aluminum at the Geneva-based World Trade Organization (WTO).
If finalized, future US deployments would be stationed in Setermoen, 420 kilometers (260 miles) from Russia.
Currently, US troops are stationed in Vaernes in central Norway, despite loud protest from Moscow.
Norway said the invitation was about NATO training and improving winter fighting capability.
"Allies get better at training together," Defense Minister Frank Bakke-Jensen told reporters.
Foreign Minister Ine Eriksen Soreide said Oslo's request had broad Norwegian parliamentary support, and insisted there would be "no American bases on Norwegian soil."
She said Oslo couldn't see "any serious reason why Russia should react, even if we expect it will again this time since it always does about the allied exercises and training."
In October, some 35,000 troops from 30 NATO members and partners, along with 70 ships and about 130 aircraft, are to be deployed for an exercise code-named Trident Juncture 18, focused on central and northern Norway, and a command post exercise conducted mostly in Naples, Italy.
'More assertive Russia'
Before becoming a founding member of NATO in 1949, Norway sought to ease Russian concerns by saying it would not station foreign troops on its soil unless it was under threat of attack.
Last February while visiting Oslo, NATO chief and former Norwegian Prime Minister Jens Stoltenberg spoke of a "more assertive Russia."
Russia and Norway share about 200 kilometers (120 miles) of land border as well as a maritime delimitation line extending across the Barents Sea and Arctic Ocean under a treaty reached in Murmansk in 2010.