The Georgian television company Rustavi 2 said Sunday an unidentified explosive device went off at a polling station in the Gala district.
But the Abkhaz security service said this information was untrue.
According to the Abkhaz security service, the explosion occurred at one of the border guard units located in the Gala district due to the careless handling of arms, as a result of which one soldier died and several others were injured.
An investigation into the incident has been launched, the Abkhaz security service said.
Georgia's breakaway region of Abkhazia holds the second round of parliamentary elections Sunday.
During the first round held March 4, Abkhaz residents elected 18 out of the required 35 deputies to the unrecognized republic's legislature. In 17 constituencies, none of the candidates gained the required number of votes.
Abkhazia declared independence from Georgia following a bloody conflict in the early 1990s. Russia helped the warring parties reach a ceasefire agreement, and has since led a post-Soviet CIS peacekeeping contingent in the region.