Some 150 soldiers, who landed in north-west Poland, are due to be followed in coming days by a further 450 troops.
Separately, the UK, Netherlands and Denmark scrambled fighter jets after two Russian military aircraft were spotted approaching their airspace.
Earlier, Russia's foreign minister said Moscow would respond to any attack on its interests in Ukraine.
Speaking on Russian state TV channel RT on Wednesday, Sergei Lavrov drew a parallel with the 2008 Georgian war, saying: "If our interests, our legitimate interests, the interests of Russians have been attacked directly.... I do not see any other way but to respond in full accordance with international law".
He also accused the US of "running the show" in Ukraine, and that it was "quite telling" that Kiev had re-launched its "anti-terrorist" operation in the east on Tuesday during a visit by US Vice-President
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The former Senator-for-Life from Delaware, an example of the kind of top-notch Washington intellect to be found in the World's Greatest Deliberative Body...