Nalbandov said Russia's actions were "aimed at further increasing tensions in the region".
Lieutenant Colonel Andrei Bobrun, a local Russian military spokesman, said: "The aim of the exercises is to establish the actual state of battle readiness and troop mobilisation deployed in Russia's southwest region."
Tensions remain high between Russia and Georgia, which lost authority over the breakaway regions of South Ossetia and Abkhazia during last year's war.
The Russian manoeuvres come as 20 unarmed observers for the Organisation for Security and Cooperation in Europe (OSCE) prepare to end their 17-year deployment in Georgia, where they have been patrolling as far as the South Ossetia border.
European security officials have warned the pullout could lead to an increased risk of separatist violence in the former Soviet state.
Another 130 United Nations monitors are also due to pull out of Abkhazia, after their mission was vetoed by Russia, leaving just 225 EU monitors watching two fronts.
Matthew Collin, Al Jazeera's correspondent in Georgia, said the withdrawal will leave the international community unable to monitor what's going on beyond this part of the conflict zone.
"With the two sides still facing each other across the ceasefire line, there are fears that this tense stand-off could once again turn violent," he said.
Speaking to Al Jazeera, Lawrence Sheets, from the International Crisis Group, an independent organisation which attempts to prevent conflicts, said: "You have a lack of trust in general, the lack of a security regime.
"I think all these things add up to a potentially explosive situation, unfortunately, which the West should be paying more attention to and the world community should be paying more attention to."
Russia has been building military bases, storage facilities for supplies, and roads in South Ossetia and Abkhazia, both of which Moscow has recognized as independent.
Around 6,000 Russian troops are based in each region.
Russia's exercises will end on July 6, the day Barack Obama, the US president, arrives for a much anticipated summit with Dmitry Medvedev, his Russian counterpart, in Moscow.