Before joining NATO in 1949, Norway allayed Russian fears by pledging not to open its territory to foreign combat troops so long as it was not attacked or threatened with attack.
The stationing of US troops in Norway "contravenes the Norwegian decision from 1949... This makes Norway less predictable, can stoke tensions, incite an arms race and lead to a destabilisation of the situation in northern Europe," the embassy wrote.
Oslo's announcement came after nine nations along NATO's eastern flank last week called for the alliance to bolster its presence in their region.
Since last year, 330 US Marines have been deployed on rotation at Vaernes in the centre of Norway, despite loud protests from Russia.
The US deployment agreement would also be extended from the current six-month renewable periods to five years.
"For this support to work in times of crises and war, we are totally dependent on joint training and exercises in times of peace," he added.
Bulgaria, Czech Republic, Estonia, Hungary, Latvia, Lithuania, Poland, Romania and Slovakia had Friday called for NATO to discuss an increased military presence in their region at next month's leaders' summit in Brussels.
The group said it was necessary to supplement NATO's current ground forces "with aerial and naval components." NATO beefed up defences in central and eastern Europe in response to growing fears about Russia, following Moscow's annexation of Crimea in 2014.
Norway has insisted that it is respecting its 1949 commitment, noting that the troop presence is not permanent but rotational.
But Moscow rejected that argument.
"Even if the actual people are rotated, the stationing is continuous," it said. Russia also expressed "concern" that the "plans were agreed in Oslo without any real bilateral political dialogue.
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