Nato has set up its headquarters at the Vaziani military base, 30km outside the capital.
Officials said on Wednesday that meetings would take up the bulk of this week, with full-scale exercises beginning on Monday.
'Show of confidence'
Moscow has denied any involvement in the mutiny at the base and has strongly criticised Georgia for hosting the Nato drills.
Dmitry Medvedev, Russia's president, described the exercises as "an overt provocation".
Matthew Collin, Al Jazeera's correspondent in Tbilisi, said tensions between Russia and Georgia look set to remain high for some time to come.
"Obviously these exercises have angered Russia which doesn't want to see Nato playing war games in what it sees as its backyard, its sphere of influence.
"From the Georgian side, this is being seen as a real show of confidence after the war last year," he said.
The Nato exercises have also increased tension between Russia and the military bloc, after ties were strained following last year's Russia-Georgia war.
Pavel Felgenhauer, a military analyst, told Al Jazeera the exercises were being seen by Moscow as "a demonstration by the West that it does not accept Russian dominance in that region".
In a further sign of souring relations, Russia on Wednesday announced the expulsion of two Canadian Nato envoys in Moscow.
| Lavrov insisted Russia wanted good relations with Nato despite the expulsions [EPA]
The Russian foreign ministry said the pair were expelled "in response to an unfriendly act by Nato against Russian envoys to Nato".
The move follows Nato's expulsion of two Russian envoys at the bloc's headquarters in Brussels on suspicion of spying, a charge Moscow denies.
In a statement, Nato said: "The Russian measure is very unfortunate and counterproductive to our efforts to restore our dialogue and co-operation with Russia.
"Thus Nato very much regrets the Russian action and does not consider there to be any justification for it."
Sergei Lavrov, Russia's foreign minister, has insisted that Moscow wants good relations with Nato despite the expulsions.
"We were forced to react. Excuse me, but those are the rules ... and our Nato colleagues, at least those who initiated the expulsion of our diplomats, couldn't have expected anything less from us," he said.
Dmitry Rogozin, Russia's ambassador to Nato, was highly critical of the military alliance in an interview with Russian newspaper Izvestia.
"This organisation is becoming more and more unpredictable ... The alliance can't seem to behave in a respectable, stable and decent way," he said.
Nato, which invited many non-member countries to take part in the games, has said the exercises pose no threat to Russia.
They are being seen as a gesture of solidarity with Georgia, which aims to become a member of the military alliance - a move also opposed by Russia.