U.S. officials are "deeply concerned" by the aviation operation, which has already begun and is expected to continue until Friday, said Jen Psaki, a State Department spokeswoman.
"Exercises of this kind are provocative and only serve to escalate tensions," she told reporters.
The exercise is expected to involve dozens of fighters, bombers and attack helicopters.
The Obama administration has accused Russia of sending military personnel and heavy arms into Ukraine to help the separatists and of shelling Ukraine from across the border. It has also accused Russia of providing the air defense system that shot down Malaysia Airlines Flight 17 last month.
Psaki said U.S. intelligence indicated Russia was poised to send heavier multiple-rocket launcher systems across the border to help the separatists fend off Ukraine's efforts to reclaim territory.
Amid the Ukraine tension, President Obama took some uncharacteristic shots at Russia, describing it in an interview as a stagnant regional power with a resource-dependent economy.
In an interview with the Economist magazine, he said it was important "to keep in perspective that Russia doesn't make anything. Immigrants aren't rushing to Moscow in search of opportunity. The life expectancy of the Russian male is about 60. The population is shrinking. And so we have to respond with resolve to what are effectively the regional challenges that Russia represents."
John Herbst, a former U.S. ambassador to Ukraine, said Obama's comments might have been intended to convince Europeans, who have been reluctant to penalize Russia over Ukraine, that the Russians "are not as strong as you think."
But he speculated that a more likely explanation was simply that the comments reflected Obama's frustration with Russian President
Though Obama has generally been restrained in his comments on Russia, "he may be feeling, 'I've had enough of this guy,' " said Herbst, who is now with the Atlantic Council.
He said that in his view, the comments were a mistake. They aren't likely to persuade Putin to reduce his pressure on Ukraine, and could undermine the administration's attempts to portray itself as the country acting with restraint.