Dmitry Vishernyov, the first secretary at the Russian Embassy in Georgia's breakaway republic of Abkhazia, was found dead with a gunshot wound to the head Monday. His wife was also wounded in the attack, Russia's state news agency RIA Novosti reported.
Investigators said Tuesday there were interviewing potential witnesses.
The Russian embassy said it was considering a number of motives for the killing, including terrorism, the state news agency said.
Russia is among the few nations that recognize Abkhazia. Georgia and Russia went to war briefly over breakaway republics in 2008.
The Russian news agency said the diplomat was working on disputes over seaside property owned by Russian citizens in the republic. RIA Novosti reported investigators have suggested the slaying may be politically motivated.
Georgia's government reacted angrily to an August visit to Abkhazia by Russian President Vladimir Putin. His visit coincided with the 5th anniversary of Russia's recognition of Abkhazia as an independent republic.