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"Shots were fired at a Georgian police post from the direction of a Russian checkpoint near the entrance to the village of Karaleti, Gori district," the Foreign Ministry said in a statement.
A policeman was shot in the head and throat and died later in ahospital, the statement said.
"This incident provides yet another proof that the Russian side continues to grossly violate the six-point cease-fire document," the statement said.
Russia denied its troops fired at the Georgian post, the Interfax news agency reported.
The accusation came two days after Russian President Dmitry Medvedev pledged to pull back all Russian troops within one month from buffer zones around South Ossetia and a second breakaway region, Abkhazia.
Georgia rolled in troops to retake South Ossetia in early August, triggering a Russian military surge that drove the Georgian forces out. Since fighting ended with a French-brokered cease-fire deal, Georgia and the West have accused Russia of failing to honor its pledge to withdraw its troops to pre-conflict positions.
Russia says its troops remaining in Georgia are serving on a peacekeeping mission agreed in the cease-fire deal.
Russia said on Tuesday it has started pulling back its forces from buffer zones near the two regions under a new deal brokered by French President Nicolas Sarkozy.