In Saturday’s first round, Robert Fico polled 28.2% with Andrej Kiska on 24% on a turnout of 43.4%.
Independent conservative Radoslav Prochazka was third with 20.8%.
As no candidate gained 50% of the votes, a second round run-off will be held in two weeks’ time for the mainly ceremonial post.
Robert Fico’s left-wing Smer party won the parliamentary election in 2012.
The 49-year-old had previously served as prime minister from 2006 to 2010, pursuing an anti-austerity agenda.
Since the 2012 elections Robert Fico’s party has governed alone – the first time since independence that a party secured an absolute majority in the Slovak parliament.
Slovakia’s president has the power to appoint the prime minister, as well as the main figures in the judiciary.
However, parliament exercises legislative power.Robert Fico’s bid for the presidency is widely seen as an attempt to make his domination of Slovak politics total.
Outgoing President Ivan Gasparovic was elected for the first of two five-year terms in 2004 as voters united against former PM Vladimir Meciar.
Slovakia adopted the euro in 2009 during Robert Fico’s previous term as prime minister.
The country has since seen significant economic growth.
Past governments had been blamed for privatization scandals and other forms of corruption.
Analysts say challenger Andrej Kiska, a 51-year-old millionaire, is riding a wave of continuing popular anger at allegations of sleaze and distrust in established parties.
Andrej Kiska says he wants to fight corruption and create a more efficient government.
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