However, he called the result an "absolute success" that gives him a right to get a chance by Ivan Gasparovic, the country's president, to form a government.
"If we fail, we will respect a right-wing government, and become a tough opposition," he said.
Fico's other current junior coalition partner, the People's Party-Movement for Democratic Slovakia (LS-HZDS), failed to enter parliament.
The major opposition Slovak Democratic and Christian Union, whose free-market reforms earned the country Nato and EU membership, won 28 seats.
Iveta Radicova, its election leader, said talks with three other parties on forming a center-right coalition will start later on Sunday. If they succeed, she has a chance to become the first woman in the post of prime minister.
"The citizens of Slovakia have voted for responsibility," Radicova said.
The opposition had pledged to improve the business environment, create new jobs, reduce the deficit and fight corruption.
Turnout was 58.8 per cent, higher than the record low of 54.7 per cent four years ago, although some parts of the country have been recovering from flooding and Slovakia has been hit by a wave of hot weather.
Despite the country's ballooning budget deficit, the campaign was dominated by debate over a new Hungarian citizenship law, not the economy.
Slovak leaders criticised a move by Hungary last month to make it easier for ethnic Hungarians in neighboring countries, including 520,000 in Slovakia, to acquire Hungarian citizenship.
Slovakia, which called dual citizenship a security risk, responded with a law allowing authorities to strip Slovak citizenship from those who become Hungarian citizens.