With almost 50% of the votes in the twin presidential and parliamentary votes counted, the central electoral bureau said on Monday the ruling Social Democrats (PSD) captured about 35% of the votes.
The centrist alliance of Liberal and Democrat parties was a close second with about 32%.
Prime Minister Adrian Nastase led the presidential race with 39%, and will face a runoff against alliance leader Traian Basescu, who won 35%.
Earlier, Romania's opposition demanded an investigation into reports of irregularities in Sunday's general election in which the ruling ex-communists won the biggest share of the vote.
Fears of vote fraud in the Balkan country, aiming to join the European Union in 2007, have been fuelled by events in neighbouring Ukraine, shaken by mass protests against what the West and the Ukrainian opposition see as a rigged election.
"Our representatives on election committees across the country have alerted the police about cases of fraud," a senior official in the Liberal-Democrat alliance, Ioan Onisei, said on Monday.
Onisei said he was not able to say how widespread the voting irregularities were, but in the run-up to the election some analysts and Western diplomats expressed concern the ruling party might use its clout to tip the close contest.
The General Prosecutor's Office in Bucharest said it had no information yet on any complaints, while the PSD has vehemently denied trying to rig the vote.
Some fear fraud is fuelled by
events in neighbouring Ukraine
The Organisation for Security and Cooperation in Europe, a pan-European watchdog monitoring human rights, has declined to comment, saying it would issue a statement later on Monday.
Previous elections held in Romania since the 1989 fall of communism have been judged fair by independent poll monitors.
Like in Ukraine, concern about the fairness of the Romanian election has centred on how absentee ballots were cast.
Vote abuse alleged
A Romanian rights group, Pro Democratia, said some of its 3300 monitors across the country saw buses full of PSD supporters touring the countryside, raising the prospect of multiple voting. The group says the irregularities it observed could affect up to 5% of the vote.
If exit polls are confirmed, the PSD will face a struggle to cobble together a majority coalition it needs to carry out EU-oriented reforms because opposition gains are set to cut into their control of parliament, analysts say.
Exit polls indicated the centrist opposition alliance, running on an anti-corruption ticket, has registered a big increase on their 2000 result.
Romanians have blamed the PSD for widespread graft, but the party's success in boosting economic growth and promises to take care of the underprivileged have carried the day, analysts say.
Coalition ruled out
Both main parties ruled out a coalition with the far-right Greater Romania party, which came third with 13%, and whose participation in any government could jeopardise ongoing membership negotiations with the EU, diplomats say.
That leaves a small party of ethnic Hungarians and a handful of deputies representing several other minorities as potential coalition partners.
Previous elections have been
judged fair by poll monitors
Analysts said a PSD minority government could complicate the party's domestic agenda, but would not necessarily hurt Romania's EU preparations, given the centrists are also staunchly pro-EU, and are seen as more reform-oriented.
The poor Balkan country of 22 million people has yet to
convince the sceptical EU that it is prepared to accelerate
reforms needed to win entry in 2007.