Both parties have been cautioned for claiming early victory
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Two men have been killed during post-election celebrations in Albania.
One man was shot outside opposition party offices in the central town of Lushnje. The second man was killed in an apparent a reprisal shooting.
Early results show the Democrats leading the governing Socialists - but final returns are not expected until later on Tuesday.
International observers have said the election did not fully meet international standards.
Monday's killings bring to three the number of deaths related to Sunday's election.
An election official was also shot dead on Sunday in the capital Tirana.
Test poll
The elections are being seen as an important test of the country's democratic credentials.
But the Organization for Security and Co-operation in Europe (OSCE) says the election complied "only partially" with democratic norms.
Officials said voting was mainly peaceful and turnout was over 50%.
OSCE election monitors said there had been limited progress since previous elections.
"The election day was generally peaceful but a few violent incidents, one fatal, cast a shadow over the process," the OSCE said in a report issued before news of Monday's killings emerged.
The main parties - the Socialists and the Democrats - were cautioned for claiming victory before polls closed.
EU bid
The EU said the conduct of the vote would determine the future of Albania's bid for membership.
The EU's foreign policy chief Javier Solana called for an investigation into the shortcomings late on Monday and urged all parties to accept the final results.
Jorgen Grunnet, head of the election observers from four international organisations, said that some of the "international standards were almost met, some almost not met, and some were in-between".
Opinion polls had showed the two main parties running virtually neck and neck. Albania has no history of reliable exit polling.
President Moisiu told Albanians the greatest outcome of the poll would be to prove the country has the ability to hold free and fair elections.
Since the fall of communism in 1991, elections have been plagued by claims of fraud.