Russia has blasted the drills, to run until June 1, as a provocation in the light of the brief war last August, when Moscow sent troops to repel Georgia's attack on South Ossetia.
Tbilisi said on Tuesday it had crushed a mutiny at a tank base, claiming Russia was behind the revolt, which was part of a coup to overthrow President Mikheil Saakashvili and thwart the NATO drills. Moscow dismissed the accusations as attempts to distract attention from almost month-long opposition protests.
The opposition, which has demanded Saakashvili step down over the war with Russia and his backsliding on democracy, said on Tuesday the coup reports were a "theatrical show" staged by the president, and "virtual reality."
"The full-scale exercise is due to begin on May 11, today we are launching its preparatory phase," Georgian Defense Ministry official David Nardzaya said on Wednesday.
Over 1,300 troops from 19 NATO member or ally states were originally scheduled to participate, but Kazakhstan, Latvia, Estonia, Moldova, Serbia and Armenia have withdrawn.
NATO has dismissed Russia's concerns about the drills, saying they were not aimed against Russia. They are designed to improve interoperability and will not involve any light or heavy weaponry, the bloc said.
NATO spokesman James Appathurai reiterated in a Russian radio interview on Wednesday that the exercise had been planned before the Georgia war, and was not a show of support for Georgia.
Russia, anxious about the Western alliance's expansion to include its former Soviet allies and new NATO bases emerging on its border, is strongly opposed to NATO membership for Georgia and Ukraine.
The two countries' bids were kept on hold at a NATO gathering in December.