On Tuesday, Georgian government forces surrounded a tank battalion that was planning an uprising, officials said. Eventually most of the unit's 500 soldiers surrendered and several commanders were detained, The New York Times reported.
President Mikheil Saakashvili said Russia had hoped to disrupt the NATO exercises.
"We are asking our northern neighbor to refrain from any provocations," Saakashvili said, in reference to Russia, during a televised interview.
Russia denied any role in the incident.
"This is not the first time we have been accused of interference without evidence," a statement from the Ministry of Foreign Affairs said. "We would like to reiterate that Russia, as a matter of principle, doesn't interfere in Georgia's domestic affairs."
The military exercises, run through NATO's Partnership for Peace program, have been a source of tension in the region. NATO officials said the exercises were routine and small-scale, but Moscow said the training was provocative because it was scheduled less than a year after Russia's war with Georgia.
Russia's NATO envoy, Dmitri O. Rogozin, warned the exercises could "significantly affect the stability of the entire South Caucasus."
Armenia, Serbia and Kazakhstan officials said their countries wouldn't participate in the exercises as a show of solidarity with Russia.
Also, Russian Foreign Minister Sergey Lavrov notified NATO that it was pulling out of a NATO-Russia Council meeting scheduled for May 19 to protest the exercises
Russia also protested NATO's expulsion of two Russian diplomats suspected of spying.
Russian media said Moscow planned a tit-for-tat expulsion of two NATO officials at the alliance's information office in Moscow.