Al Jazeera's Matthew Collin, speaking from the Georgian capital Tbilisi, said: "With about half the vote counted, [Yedinstvo] look set to win these elections as expected."
About 50,000 South Ossetians were eligible to vote in the elections and polling stations have been set up in Russia for expatriates and refugees who fled the region during the war.
Four parties are competing for the 34 seats in parliament but the central election commission has barred the only two parties not loyal Kokoity.
Alan Gassiyev, an opposition leader, called the polls "completely illegal".
"I plan to sit at home. There's nothing we can do," he said.
The opposition has also accused Kokoity of embezzling funds allocated for restoration of infrastructure destroyed in the war.
Kokoity has rejected the accusations against him as Georgian propaganda.
He pledged that the vote would be carried out strictly in accordance with law, calling the election a "maturity test for the small independent state".
"At 10am [06:00 GMT] I can already say there's a very high turnout," Kokoity said on Sunday.
Most world powers consider South Ossetia as part of Georgia, but Tbilisi lost control over the region in a war in the early 1990s as the Soviet Union fell apart.
Many South Ossetians feel closer to Russia.
Describing the current situation, our correspondent said tensions remain high on the disputed border around South Ossetia.
"You've got the Georgian army on one side and the Russian army on the other, which means you've got the constant possibility of renewed fighting," he said.
"South Ossetia is basically propped up by Russia. It is a tiny area that could only ever survive with Russian military, economic and political support.
"And I think everyone on both sides were expecting to see the current South Ossetian regime to be maintained.
"The question is, where do we go from here and will the tensions are around the border area erupt again into violence."