Abkhazians are electing a new 35-seat legislature, with 108 candidates running for parliament in single-mandate constituencies.
As of 2:00 p.m. Moscow time (11:00 a.m. GMT), 35% of registered voters had come to the polls, crossing the electoral threshold of 25%, the commission said.
The separatist republic's 190 polling stations opened at 08:00 a.m. Moscow time (05:00 a.m. GMT) and will close at 8:00 p.m. (5:00 p.m. GMT), the commission said.
President of Abkhazia Sergei Bagapsh said Saturday the Abkhaz leadership is taking all measures to ensure law and order and provide security for civilians, despite Georgia's attempts to disrupt the parliamentary elections.
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.
At the same time, Georgian President Mikheil Saakashvili condemned the parliamentary elections in the separatist region as illegitimate.