Georgia said a raiding party from Abkhazia had attacked Georgian guards who were protecting a road being built in the Kodori Gorge.
Meanwhile, Abkhazia said a Georgian military group had entered the republic's territory and killed two Abkhazians.
Tbilisi later expressed its concern over the incident and accused Abkhazia of "armed provocation."
Mutual accusations of violating a ceasefire regime have been frequent from both Abkhazia and Georgia, whose President Mikheil Saakashvili has vowed to regain control of the region. Peace talks broke off when Tbilisi sent troops into Kodori in July and established a parallel Abkhaz administration there.
Abkhazia declared independence from Georgia following the collapse of the Soviet Union in 1991, sparking a bloody conflict in the region.
Russia mediated ceasefire agreements between the sides, and Russian peacekeepers have been deployed in the conflict zone ever since.