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Moscow has denied "threatening" Ukraine and, for its part, has threatened "measures" should Western states send armed forces into the country.
"Russia threatens no one and has never threatened anyone," Kremlin spokesman Dmitry Peskov told journalists on Friday.
He was responding to the US government's sharp criticism of the alleged Russian troop transfer to the border with Ukraine.
Regarding a possible Western troop transfer to Ukraine, Peskov said that "such a scenario would undoubtedly lead to a further increase in tensions near the Russian borders".
"Of course, this would require additional measures on the Russian side to ensure Russian security," he added.
Ukrainian President Volodymyr Selenskyj accused Russia on Thursday of having increased its troop presence on the border with Ukraine.
Moscow wants to create a "threatening atmosphere".
Ukrainian military intelligence accused the Russian army of wanting to expand its presence in the Donetsk and Luhansk regions controlled by the pro-Russian rebels.
Washington warns Moscow against attempted intimidation
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Washington expressed concern at the reports.
US State Department spokesman Ned Price condemned the "recent escalation of the aggressive and provocative actions by Russia in eastern Ukraine" and warned Moscow against attempts to "intimidate or threaten our partner Ukraine".
According to Kiev, US Defense Minister Lloyd Austin promised his Ukrainian colleague Andrej Taran in a phone call not to leave Ukraine "in the event of escalating Russian aggression".
In the conflict over eastern Ukraine, which has been going on since 2014, more than 13,000 people were killed.
Russia rejects the allegation that it provides military support to the rebels in the region.
In July last year, the conflicting parties agreed on a ceasefire.
Since mid-February, however, there has been increased fighting that undermines the already fragile ceasefire.