The Georgian television report said that a group of approximately 10 assailants attacked the building, located close to the village of Chuburkhinji in the Zugdidi region, with a grenade launcher, before opening fire with assault rifles.
Local police said that the attackers fled into territory controlled by Abkhazia, with eyewitnesses claiming they headed in the direction of a Russian peacekeepers' base.
The building was damaged, but no casualties have been reported.
A spokesman for the Russian peacekeepers contingent confirmed that an incident had occurred in the region, near the de facto border between Georgia and breakaway Abkhazia, but declined to give any further information until an investigation had been carried out.
On July 6 in the Zugdidi region, four bombs went off as Georgian police vehicles were travelling along a road near the village of Rukhi. One of the cars was damaged, but no one was injured.
Russia submitted a draft resolution to the UN Security Council on Tuesday on the situation in Georgia, amid escalating tensions in the country's breakaway regions of Abkhazia and South Ossetia.
Abkhazia claims that Georgia is responsible for a series of explosions that have rocked the de-facto independent republic since June 30. The most recent blast hit a cafe on Sunday in the town of Gali, on the Georgian-Abkhaz border, killing four and injuring six.
Russia provides aid to Abkhazia and recently sent additional troops into the area, saying they were needed to deter new bloodshed. The pro-Western Georgian government of Mikheil Saakashvili has accused Russia of trying to annex the breakaway republic, along with another Georgian rebel republic of South Ossetia.
Abkhazia 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 subsequent fighting.
