Among the main contenders are the Socialist Party of Albania, the Democratic Party of Albania and the Socialist Movement for Integration.
"The Socialist Party might have won more than 71 seats (in the 140-seat parliament), but this is still an opinion not a certainty", IPR Marketing's Antonio Noto said.
Albanians were voting Sunday in a general election that follows a landmark agreement between the country's two biggest political parties to look past their bitter differences and back efforts for Albania to eventually join the European Union.
The election commission said it was extending the voting period by an hour until 8:00pm (1800 GMT) owing to poor turnout, while Socialist Prime Minister Edi Rama posted repeated messages on Twitter and Facebook urging people to cast their ballots.
The risk is that Albania's newly elected president Ilir Meta may once again hold the role of kingmaker.
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When the polls closed, the preliminary turnout from the 19 percent of stations reporting participation figures was 43.9 percent, compared to 53.5 percent four years ago.
The Interior Ministry also reported hundreds of attempts to buy votes, a crime that may result in a jail term.
"I expect a radical change, a better future for the Albanians so they don't emigrate throughout the world", Tirana resident Petrit Sulo said after casting his ballot.
The largely Muslim country is celebrating Eid al-Fitr, at the end of the holy month of Ramadan.
"I came to vote for Eddie Rama because I see his hand in every corner of the country", a Rama supporter said in Tirana.
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He believed a possible outcome was a "grand coalition" between the two main forces in the 140-seat parliament - pointing out that the overriding aim of both sides is to open European Union accession talks. They have not said whether they might rule together in coalition.
Since taking office, the Socialists have managed to improve tax collection and boost the performance of the electricity sector. Economic growth accelerated to 3.45 percent previous year, compared with 0.97 percent in 2013. The country's global reputation was tarnished by data showing Albania had become Europe's biggest open-air cannabis producer.
"Today, Albania needs God more than ever", Rama said.
Both parties are keen to gain a majority so they can push through reforms aimed at smoothing the path for entry into the European Union - primarily a reform of the country's corrupt judicial system.
Rama said last month the Balkan country could get a green light for formal talks to start at the end of this year.
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An AFP journalist said small groups had begun gathering at Taksim Square but a heavy police presence outnumbered the activists. A statement also said the governor's office had not received a valid parade application - a claim rejected by organizers.
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