"At approximately 1 p.m. [10:00 GMT] a group of Georgian saboteurs attempted to cross the border near the village of Soberiya. They were noticed and there was a skirmish as a result of which one of the Georgians was killed and three were wounded," said Ruslan Kishmariya, the Abkhazian president's representative in the Gali district.
The shootout occurred when a border guard patrol came across an armed group of six people, police spokesman Lourens Kogoniya, adding that the Georgians fled back across the de facto border to the undisputed part of Georgia.
Kishmariya said the Abkhazian authorities were strengthening the border with Georgia, which he accused of continuing subversive activity.
"The Georgian special services have one goal - to find out how Abkhazia is strengthening the border with Georgia," he told RIA Novosti.
Abkhazia broke away from Georgia in the early 1990s following the collapse of the Soviet Union in an armed conflict that claimed thousands of lives.
Russia and Georgia fought a five-day war after Georgia attacked another breakaway republic, South Ossetia, on August 8. Moscow recognized Abkhazia and South Ossetia as independent states in late August. The majority of residents in both provinces have had Russian citizenship for a number of years.