The ruling Communist Party appears to be slipping behind opposition parties as results come in from the country's parliamentary election.
With 76% of votes counted, the Communists have 45.9%, while the four main opposition parties total 49.8%.
This result would give the Communists only 49 of the 101 seats in parliament.
The poll was the second parliamentary election in four months, with memories still fresh of the violence that followed the first poll.
The Communists won too few seats to elect a successor to outgoing President Vladimir Voronin, who is standing down after two terms in office, and a new poll was held to break the deadlock.
Mr Voronin said the voting had been conducted in a democratic manner.
"This is the most important achievement - that we were able to organise civilised and democratic elections," he said.
The BBC's Tom Esslemont in the capital Chisinau, says this election was always going to be on a knife edge.
The five most popular parties have campaigned for closer ties with the European Union, but critics of the Communist Party say it has failed to act on its promises during eight years in power and it is time for change and modernisation, says our correspondent.
"Democracy and truth has finally been victorious. We fought for this for so long and with so many difficulties," said Vlad Filat, leader of the Liberal Democrats who are lying second with 16.1%.
Party leaders said they planned to seek a coalition with three other oppositon parties: the Liberal Party, the Democratic Party and the Our Moldova Alliance.
However, the leader of the Democrats, Martin Lupu, could decide to co-operate with the Communist Party, of which he is a former member.
But Mr Lupu insists there can be no deal unless Mr Voronin leaves politics.
Negotiations may be necessary for the election of a new president, because even a four-party opposition bloc would lack the necessary three-fifths majority needed to elect a new leader.
Opposition parties claim the first election, held in April, was rigged in favour of the Communists.
The result, in Europe's poorest country, prompted thousands of people to take to the streets, clashing with police and storming parliament.
Assessments of April's vote were mixed. Some international observers reported flaws but others found it generally fair.
More than 3,000 foreign and Moldovan observers were supposed to be monitoring Wednesday's re-run, though one group pulled its 140 monitors out because some were barred, causing a storm of protest.
The Central Electoral Committee said the voting rate was ahead of that in April, and that a third of voters had posted ballots by early afternoon.
The Communist Party won only 60 of parliament's 101 seats in April - one short of the 61 seats needed to elect a new president. The opposition parties united to make sure the 61 target was not met, forcing parliament to be dissolved.
Mr Voronin's successor will lead a country where the average wage is just under $250 (£151) a month, and will inherit an unresolved conflict over the breakaway region of Trans-Dniester.