Results are expected within the next 48 hours. More than 250,000 security personnel across the country were tasked with protecting the vote.
While Russian President Putin remains popular, United Russia party has seen its support drop as living standards decline following years of economic stagnation.
The Balkan country will hold its third parliamentary elections and the first round of the regular presidential election on the same date, Bulgaria's President Rumen Radev says.
Early results from a post-war snap parliamentary vote in Armenia showed Prime Minister Nikol Pashinyan's party leading with 58.5 percent of the vote, far ahead of ex-president Robert Kocharyan's alliance with 18.5 percent.
Support for PM Boyko Borisov's GERB party has been eroded by a series of scandals, with protests last year accusing the government of protecting oligarchs.
PM Nikol Pashinyan says he will resign so that snap elections can take place in the coming month.
The parliamentary election included run-off votes in 49 electoral districts and first round voting in 69 districts where violence stopped the vote from taking place in December.
The election is the sixth parliamentary poll for Europe's youngest country since 2008, when it declared independence from Serbia.
Nur Otan party led by powerful ex-president Nursultan Nazarbayev sweeps parliamentary election, exit poll shows, as it has done for decades, with no major opposition groups running in the vote.
Tensions boil over during tightly contested presidential and parliamentary elections that both sides say they are on track to win.
Voters are participating in elections set to keep parliament in the hands of tribal and pro-government deputies, as Amman grapples with its worst economic crisis in years.
Georgians go to polls to elect a new parliament in a country seen as a rare example of democracy among ex-Soviet countries.
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