Both Traian Basescu, pictured, and Mircea Geoana have claimed victory
Romania's opposition Social Democrat party says Sunday's presidential election was rigged and plans to contest the result.
Official results showed incumbent President Traian Basescu with a winning margin of less than 1%.
Earlier, exit polls had predicted victory for his Social Democrat rival, former Foreign Minister Mircea Geoana.
Both candidates had claimed victory on Sunday night in what correspondents describe as a bitter contest.
"We have proof of fraud," Social Democrat vice-president Liviu Dragnea was quoted as saying by Reuters news agency.
"The exit poll, the large number of annulled votes... massive electoral tourism and other things obviously force us to contest the result."
Election officials said centre-right President Basescu had won 50.3% of votes compared to Mr Geoana's 49.7%.
Election observers from the Organisation for Security and Cooperation in Europe said Sunday's voting had generally met commitments made, but urged authorities to investigate reports of irregularities.
The election campaign was fought against the backdrop of a serious economic crisis in Romania. It has also been marred by personal attacks and allegations.
A TV debate ended in smiles and handshakes despite a bitter campaign
Mr Geoana had told his jubilant supporters in Bucharest after the polls closed on Sunday night: "Our victory is the victory of all Romanians who want a better life. This is a beautiful night for Romanian democracy."
But Mr Basescu also claimed victory, saying exit polls were deceptive.
"I won. I assure you that... the correct polls showed that I was ahead of Mircea Geoana," he said.
"My voters need to stay calm and convinced that the counting of votes cannot be subject to fraud."
One of the key roles of the next president will be to appoint a prime minister, as Romania has been led by a caretaker government since October.
The International Monetary Fund (IMF) has delayed the payment of part of a 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.
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