PM Robert Fico is seen as the frontrunner, ahead of businessman-turned-philanthropist Andrej Kiska.
Opinion polls predict a two-candidate run-off vote will follow as no one is expected to win an outright majority.
Robert Fico’s leftist Smer party won over half of the seats in parliament in the 2012 general election.
The Slovak president has the power to appoint the prime minister, as well as the main figures in the judiciary.
However, it is a largely ceremonial role and parliament exercises legislative power.
Outgoing President Ivan Gasparovic was elected for the first of two five-year terms in 2004 as voters united against former nationalist PM Vladimir Meciar.
Slovakia adopted the euro in 2009 during Robert Fico’s previous term as prime minister.
The country since has seen significant economic growth.
Past governments been blamed for privatization scandals and other forms of corruption.
Analysts say Andrej Kiska is riding a wave of continuing popular anger at sleaze and distrust in established parties.
The 51-year-old is a successful businessman-turned-philanthropist who says he wants to fight corruption and create a more efficient government.
Other candidates in Saturday’s vote include actor Milan Knazko, who was a leading figure of the 1989 Velvet Revolution that ended Communist rule in Czechoslovakia, and Radoslav Prochazka, an independent conservative lawmaker with a degree from Yale Law School.
Saturday’s first round is unlikely to produce an outright winner, who would need over 50% of the vote, but is expected to send Robert Fico and Andrej Kiska into a run-off on March 29.
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