Mr Geoana, right, trails incumbent Mr Basescu, left, by 3%
A run-off vote is expected in Romania after none of the 12 candidates won outright in the first round of Sunday's presidential election.
With three quarters of votes counted, centre-right President Traian Basescu has secured around a third of votes.
His main rival, Social Democrat Mircea Geoana, trails him by 3%.
Amid political crisis, Romania has been in the hands of a caretaker government since the fall of PM Emil Boc's centre-right government in October.
The winning presidential candidate will appoint a new premier and have an influence on long-delayed reforms aimed at bringing the Eastern European country up to EU standards.
The IMF has delayed the payment of part of its bail-out loan because of the current lack of effective government in Romania.
Analysts say corruption is still widespread, nearly three years after the country joined the EU.
A run-off vote pitting Mr Basescu against Mr Geoana is expected to be held on 6 December.
More than 18 million people were eligible to vote
Until then, a tough fight can be expected between the two main candidates for the votes which went to other nominees, says the BBC's Nick Thorpe in Bucharest.
While casting their votes, the two front-runners said the election was one of the most important the recession-hit country has had to face.
On Sunday, a referendum was also held to decide whether to scrap one of the two chambers of parliament and reduce the number of deputies.
Results suggested strong backing for the proposal to abolish the Senate.
There were reports of potential fraud. More voters than normal appeared to be casting their vote at special centres set up for citizens who were away from their normal residences because they were travelling, the Associated Press news agency reported.
More than 305,000 people were expected to vote at these type of locations according to the electoral committee.
However, Adriean Videanu, the country's economy minister said election authorities in Moara Vlasie were "overwhelmed" because of "electoral tourism", AP reported.
This is Romania's first presidential election as a member of the European Union. More than 18 million people were eligible to vote.
Mr Basescu, who has been president for five years, wants a mandate to overcome what he says is the blocking of his political reforms by opposition parties.
Mr Geoana - a former ambassador to the US and foreign affairs minister - is offering voters an ambitious economic stimulus package.