There are growing fears that President Vladimir Putin may be preparing to follow up the annexation of Crimea with a move into Moldova's mainly Russian-speaking separatist Transdniestria.
US Air Force General Philip Breedlove, Nato's Supreme Allied Commander Europe, said Russia had used "snap" military exercises apparently as a tactic to shift vast numbers of troops towards the border.
Around 10 days ago Moscow launched a new exercise, involving 8,500 artillery troops, near the Ukrainian border - as it had done in the days before Ukraine lost the Crimea region.
Breedlove said the Russian tactic should lead the 28-nation Western military alliance to rethink the positioning and readiness of its forces in eastern Europe so that they were ready to counter Moscow's moves.
"A snap exercise puts an incredible force at a border. The force that is at the Ukrainian border now to the east is very, very sizeable and very, very ready," he said, speaking at an event held by the German Marshall Fund, a thinktank.
"You cannot defend against that if you are not there to defend against it. So I think we need to think about our allies, the positioning of our forces in the alliance and the readiness of those forces ... such that we can be there to defend against it if required, especially in the Baltics and other places."
Ukraine is not a Nato member, but Moscow's intervention in Crimea has caused particular alarm in several ex-Soviet Baltic republics - which are.
Breedlove said Nato had attempted to make Russia a partner, but added: "Now it is very clear that Russia is acting much more like an adversary than a partner."
He voiced concern that Russia could have Transdniestria in its sights after Crimea, saying that, in Russia's view, the separatist region of Moldova was the "next place where Russian-speaking people may need to be incorporated."
In Moscow, Deputy Defence Minister Anatoly Antonov said Russia was complying with international troop limits near the border with Ukraine, and international inspectors had conducted missions in the last month to check on Russian troop movements.
"We have nothing to hide there," Antonov was quoted by the state RIA and Itar-Tass news agencies as saying.
And speaking this morning on the BBC's Andrew Marr Show, Moscow's ambassador to the EU said his country did not have any "expansionist views", and that "nobody should fear Russia".
Asked whether he could rule out a military incursion into Ukraine beyond the Crimea, Vladimir Chizhov said it was not Russia's "intention", but added that he could not speak for "the Commander in Chief".