Smer, led by Robert Fico, faces an uphill struggle to form a coalition government after failing to win an outright majority in Saturday's election, the first since the country joined the European Union in 2004.
Full provisional results showed Smer won 29% of the votes and the party of Mikulas Dzurinda, the prime minister, secured 18%. Long coalition talks are likely and Dzurinda might yet hang on to power if Fico fails to find any partners.
The talks will decide the future of reforms which included the introduction of a flat tax rate, which won plaudits from abroad and transformed Slovakia into one of Europe's fastest growing economies.
Talks could also determine whether Slovakia adopts the euro in 2009 as planned.
Promising to rein in reforms he says have left many people behind, Fico said: "Fast economic growth will no longer be for the benefit of a narrow group of people."
He said he would try to woo centre-right parties that have traditionally been allied to Dzurinda rather than make advances to fringe groups such as a nationalist party which came third with 11.7% of the votes.
"We confirm January 1, 2009, as the euro date but in case it's not favourable for the country, we could think about revising it"
Robert Fico, Smer leader
"We want a centre or centre-left government that will establish solidarity and reduce the differences that have grown between economic groups because of eight years of Dzurinda's reforms," he said during a televised debate.
Fico said he would respect Slovakia's target of adopting the euro in 2009, but left the door open to a revision of the date.
"We confirm January 1, 2009, as the euro date, but in case it's not favourable for the country, we could think about revising it," he said.
Ivan Gasparovic, the president, is likely to first ask Fico to form a government and, if he fails, then turn to Dzurinda.
Dzurinda, eastern Europe's longest-serving leader after eight years at the helm, refused to accept defeat.
The combined vote for Dzurinda's Democratic and Christian Union and his two most obvious allies was just over 38%, and he would need one more partner to gain a majority in the 150-seat parliament if Fico fails in his bid.
Dzurinda urged the two parties - the Ethnic Hungarian Party and the Christian Democrats - to stick together, keep Slovakia on the reform path and resist Fico's approaches.