After receiving the note, Vyacheslav Kovalenko told journalists that, "Russia has in no way violated the provisions and agreements that concern the presence of peacekeepers."
Moscow has increased the number of Russian peacekeepers in Abkhazia to 3,000 from 2,000, but has said that this is within the limits envisioned by earlier agreements on the number of peacekeeping troops signed by the Georgian leadership.
Abkhazia, alongside another Georgian breakaway republic, South Ossetia, broke away from Georgia in the early 1990s following the collapse of the Soviet Union. Between 10,000 and 30,000 people were killed in the Georgian-Abkhazian conflict and some 3,000 in Georgian-South Ossetian hostilities. Georgia is looking to regain control over the two de facto independent republics.
Tensions between Moscow and Tbilisi have been escalating rapidly since Russia's outgoing President Vladimir Putin called for closer ties between Moscow and the two breakaway republics in mid-April. Tbilisi also accused Russia of shooting down a drone on April 20 - a claim Russia flatly denied, calling Georgia's video footage fake.
Russia has threatened to use force if Georgia employs "violent measures," against its peacekeepers or Russian nationals living in Abkhazia or South Ossetia.
Russia's Foreign Ministry released a statement on Wednesday defending the increase in peacekeepers, saying it was "aimed at ensuring the basic rights of Abkhazia and South Ossetia's residents."
NATO spokesman James Appathurai said on Wednesday that NATO believed that while Russia may technically have the right to do increase troop numbers, "in the political reality, this is not easing tensions, it is raising tensions."