Around 3.1 million voters were eligible to vote in the seventh elections since the fall of communism in the early 1990s, with some 4,000 candidates vying for 140 parliament seats.
The poll comes almost three months after Albania joined the Nato military alliance and took its first small step towards joining the EU by submitting its candidacy for membership.
Surveys show the race is likely to be too close to call between the governing Democratic Party of Prime Minister Sali Berisha and Edi Rama’s opposition Socialist Party.
Casting his ballot at a Tirana school, Berisha said: “With these elections, which will be free and fair, Albanians will sign (their support) for the European project.”
His rival Rama said he expected Albanians to “express their will with maturity, and calmly”.
“The vote is the only possibility to make history and today every Albanian has such an opportunity,” said Tirana mayor, Rama.
President Bamir Topi said the vote “will show the world our country wants to consolidate democracy in order for Albanians to be able to circulate freely through Europe, with which Albania is determined to integrate.”
All elections in Albania have been disputed and sullied by violence since the collapse of the country’s isolationist communist regime in 1991.
And five hours after polling opened, no major incidents were reported, but the Central Electoral Commission warned parties against using any means to intimidate voters and their right to cast ballots in secrecy.
“According to information we have got so far, the situation is relatively calm,” said Richard Bosch of the OSCE.
Incidents were already registered ahead of the vote, as three people were killed during campaigning, with the murder of Socialist deputy Fatmir Xhindi in early May topping the list.
Arrests have been made in connection with the other murders, which included that of a Democratic Party activist and a northern regional leader of the opposition Christian Democratic Party.
Scrutinised by 3,000 observers, the poll is to be held in accordance with a new electoral law adopted at the request of the EU and wider international community.