"The Social Democrats won the elections and will lead the next government," Mircea Geoana, the PSD party leader, said.
There is no reason to ignore the voters' will, which was clearly expressed," he said, calling on all political parties and Basescu to an "open dialogue" on forming a new government.
But Emil Boc, the Liberal Democrat leader, disputed the claim, insisting that voters had "rejected leftist policies as a solution to the crisis that awaits us".
"No party got more than 50 per cent of the votes this evening, but if there's a winner, it's the right," he said.
The elections came as Romania tried to weather the global economic crisis, with labour disputes looming and the prospect of a recession.
Voter turnout for the elections was low, with only 34.38 per cent of at least 20 million people making it to the voting polls three hours before they closed.
Tariceanu issued an emergency press conference minutes before polls had closed, urging Romanians to vote.
He said: "The poor presence at the polls that has been seen all day today will displease many Romanians when they see the results of the vote, because they chose not to exercise their fundamental right."
All 315 parliamentary seats and 137 senate seats were up for grabs in the election, Romania's first general election since it joined the European Union along with neighbouring Bulgaria in 2007.
For the first time senators and deputies were elected in a single round of voting, using a combination of party and candidate lists.
The EU has criticised corruption and organised crime in Romania, with the European Commission calling for stronger courts and more efficient administrative systems to combat the problem.
Bucharest has undertaken some reforms, but critics argue they are far from sufficient to tackle the scourge of corruption in business and political life.
Several of its top politicians have been indicted on graft charges but their trials have been blocked by parliament or mired in court proceedings.
"There is quite an important chance the PSD will get into the next government," Alina Mungiu Pippidi, a researcher at the Romanian Academic Society think tank, said.
"For fighting corruption, the situation is pretty bad."
Some economists have warned that the prospect of tough coalition talks and a Liberal Democrat government bode ill for efforts to insulate its economy from the financial crisis.