Local police said the blast went off in a cafe late on Sunday in the town of Gali, on the Georgian-Abkhaz border. The attack follows a series of blasts early last week, which Abkhazia also blamed on Georgia's security service.
An Abkhaz security official along with a local woman died on the spot, while an interpreter for the United Nations mission and a border trooper died later in hospital, a police spokesman said.
The other six people injured in the explosion are in a stable condition, he said.
The head of Abkhazia's security service, Yury Ashuba, accused Georgia of orchestrating the attack.
"The incident in Gali is nothing but a terrorist attack aimed against security service officers working in the district. The involvement of Georgia's security service in this crime is obvious," he told RIA Novosti.
The incident follows two sets of explosions in the breakaway province on June 30 and July 1, when six people were injured in the capital, Sukhumi, and the Black Sea resort of Gagra. Abkhaz authorities blamed both incidents on Georgian security forces and closed the de facto border with Georgia. Tbilisi dismissed the accusations as absurd.
Abkhazia has been the focus of ongoing tensions between Russia and Georgia, which seeks to regain control over the province. Russia provides financial aid to the self-proclaimed republic and has thousands of peacekeepers deployed there.
Georgia has accused Russia of attempting to annex Abkhazia, along with another breakaway province, South Ossetia.
