Relations between Moscow and Tbilisi have drastically deteriorated since the Kremlin called for closer ties with Georgia's breakaway regions in mid-April.
"We hope to overcome the crisis caused by Russia's recent steps regarding Georgia's territorial integrity. I am not ruling out that some of this pressure was linked to the upcoming elections," Mikheil Saakashvili told journalists after casting his ballot.
Moscow has bolstered the number of its peacekeepers in Abkhazia, but said the increase was still within previously agreed limits on troop numbers.
The measure followed reports of a build-up of Georgian forces on the border with Abkhazia and the shooting down of Georgian surveillance drones by Abkhaz air defense.
Saakashvili reiterated his calls for integration of the separatist regions. "Russia offers them rusty tanks and total control over their destiny and property. What we offer is a transparent democratic system, a free economy and opportunities for society as a whole not for a handful of people. This is more proof that Georgia is a country open to all ethnic groups and belonging to all of them," the Georgian president said.
Saakashvili said: "Everybody in Georgia should understand that our enemies as well as our partners are watching the election," Saakashvili said.
The Georgian Interior Ministry confirmed Wednesday that several people were injured in two bus blasts in the Georgian-Abkhazian conflict zone. A shootout has also been reported between Georgian police and police from the breakaway region.