"The exit poll, the large number of annuled votes ... massive electoral tourism and other things obviously force us to contest the result," she said.
Exit polls after voting ended late on Sunday had given Geoana the lead by up to three percentage points.
Millions of Romanians voted in the decisive round of the elections.
In the first round on November 22, Basescu captured 32.4 per cent of the vote while Geoana secured 31.2 per cent.
Basescu was endorsed by the ruling Democratic-Liberal Party (PDL) while Geoana was supported by the Social Democratic Party-Conservative Party Alliance (PSD), as well as the National Liberal Party and the Hungarian Democratic Union of Romania.
Both men claimed they had the solutions to lift Romania out of a recession, form a government, eradicate corruption and restore public trust.
But neither candate gave figures on their economic plan for the country,
Romania's budget deficit is set to hit 7.3 per cent of GDP by the end of 2009.
The International Monetary Fund (IMF), the EU and the World Bank agreed in March to provide a $30bn loan to the country to help ease its economic crisis.
But the two lenders withheld payments in November following the collapse of the ruling coalition comprising Basescu's PDL and Geoana's PSD.
An interim administration has ruled Romania since the coalition fell apart.