"The steps that have been taken and the rhetoric have increased tensions and undermined Georgia's territorial integrity," NATO spokesman James Appathurai told reporters in Brussels.
He called on both Moscow and Tbilisi to steer clear of inflammatory rhetoric.
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.
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 as "aimed at ensuring the basic rights of Abkhazia and South Ossetia's residents" and said it was in line with international agreements.
Appathurai said 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."
A RIA Novosti correspondent reported from Abkhazia that the Russian peacekeeping contingent in the region has been increased by 50% to 3,000 servicemen, as envisioned by the Moscow agreement on a 1994 ceasefire.
Georgia's Foreign Ministry confirmed that Russian military hardware and troops had already crossed the border into the breakaway republic of Abkhazia and called the move "an act of aggression."
Russia has claimed that Georgia has massed troops on Abkhazia's border in preparation for a military operation.
The chairman-in-office of the Organization for Security and Cooperation in Europe, Alexander Stubb, said the OSCE was seriously concerned over the recent events in Georgia, including Russia's decision to strengthen ties with the two breakaway regions and the drone incident.
