"A Georgian mortar platoon is shelling southern districts of Tskhinvali," South Ossetia's information and press committee said. "The northern [de facto] border is also being shelled. South Ossetia is returning fire."
South Ossetia had earlier reported that Georgian snipers were firing on a border checkpoint in the region, killing one police officer and injuring one more.
Russian peacekeepers deployed in the region confirmed the reports of automatic weapon fire.
"Three people have been killed and seven injured as of 21:00 Moscow time (17:00 GMT) by snipers from the Georgian side firing on Tskhinvali," Commander Vladimir Ivanov said, adding that the attacks were continuing.
South Ossetia's leader said the unrecognized republic would retaliate.
"Georgia has declared a sniper war on the Republic of South Ossetia and made another attempt to unleash a large scale war," Eduard Kokoity said. "The republic has so far refrained from retaliatory moves, but will not do so any more."
Tbilisi has not yet commented on the reports.
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Ukraine has not preserved its 1991 borders. The signing of the Geneva memorandum on April 17 reaffirmed the willingness of Russia, the United States and EU countries to reach a compromise. While the sides continue to trade tough talk and symbolic sanctions, the Kremlin and the White House are also holding a parallel dialogue on the coordinated geopolitical revision of Eastern Europe.