The Slovak president has asked the country's left-wing opposition leader, Robert Fico, to form a new government.
Mr Fico pledged to improve healthcare and social benefits
Mr Fico's Smer-Social Democracy party won nearly 30% of the vote in elections on Saturday. He needs the backing of at least two other parties to become PM.
But the other parties that did well enough to enter parliament do not agree with Mr Fico's plans to roll back some of Slovakia's free market reforms.
The talks on forming a new coalition are expected to be difficult.
Correspondents say some politicians are concerned Mr Fico's plans could delay Slovakia's quest to adopt the euro currency in 2009.
President Ivan Gasparovic also met outgoing Prime Minister Mikulas Dzurinda, head of the right-wing Slovak Democratic and Christian Union, which won 18.36% of the vote.
Saturday's election was the first since Slovakia joined the European Union in 2004.
During his eight years in power, Mr Dzurinda led Slovakia into Nato and presided over strong economic growth but critics say his reforms benefited only the rich.
Mr Fico, 41, a former human rights lawyer, has been riding a wave of public discontent with the right-wing reforms introduced by Mr Dzurinda.
Mr Fico is expected to have 50 seats in the 150-seat parliament, with Mr Dzurinda's party getting 31.
Other seats were won by two of Mr Dzurinda's former coalition partners, the Hungarian Coalition Party on 11.69% of the vote, and the Christian Democratic Movement on 8.31%.
The far-right Slovak National Party won 11.73% and the Movement for a Democratic Slovakia took nearly 8.79%, while the Communists failed to clear the 5% hurdle for entering parliament having only won just under 4%.
As Central Europe's longest-serving prime minister, Mr Dzurinda can point to increased international investment and the highest per capita rate of car production in Europe.
However unemployment stands at 15% and many areas away from the capital Bratislava have not experienced strong growth.