The main parties disagreed on Sunday (8 May) over whether the elections had met EU standards, and a 525-strong international election observation team was due to issue its assessment on Tuesday after monitoring polling booths across the country.
Democracy is just 20 years old in Albania, which is still suffering post-Communist growing pains. Four people were shot dead in January when anti-government protests turned violent (see 'Background').
The opposition Socialists have refused to accept the result of the 2009 election that gave Prime Minister Sali Berisha a second four-year term and accuse his government of corruption.
Sunday's vote was the first test of support for Berisha's government since the election. Campaigning was marred by explosions and scuffles.
"I hope the counting process will go well, just like the election day," said Central Election Commission chairman Arben Ristani, mindful of problems with counting after past elections.
Berisha, under EU pressure to provide proof that the Balkan nation is a functioning democracy, rushed to call Sunday's polls "the best elections ever held".
'Calm and dignified' election
"I am here to greet all citizens for voting in the most European way in their history. The election was calm and dignified [...] and had a high turnout," Berisha said.
"These were the best elections on the screens. But they were the ugliest in the reality of common people," opposition Socialist leader Edi Rama said shortly afterwards.
"The election process provided spectacular examples and evidence of a mismatch with international standards," he added.
Each side claimed victory, but neither was celebrating.
More than 50.9% of voters cast their ballots calmly. The parties traded charges of irregularities and threats, but avoided angry outbursts often seen in the past.
Pictures of one poll official with blood on his face, another attacked by a party official, and three attacks on television crews tarnished an otherwise calm voting day.
The European Union rejected Albania's application to become a candidate for membership last November. It has made clear the vote must be free and fair if Albania, a NATO member, wants to be considered for candidate status by the end of this year.
The European Union has also told Albania's feuding political parties they must negotiate an end to the row over the 2009 election that is holding up legislation in parliament.
"Albania cannot miss the opportunity to demonstrate that it is conducting elections in line with European and international standards," EU Enlargement Commissioner Štefan Füle said.
A top-level EU team will visit Albania in late May.
Police, who deployed about 7,000 officers near the 4,891 polling stations, had taken most ballot boxes to counting centres by midnight, a spokeswoman said.
They arrested a dozen youths, led by a former convict wearing a bullet-proof vest, who were intimidating voters in a Tirana suburb with guns and knives.
(EurActiv with Reuters.)