Some 4.4 million Slovak voters were called on to elect a new head of state on Saturday as polling stations opened their doors at 7 am (0600 GMT).
Voting was to end at 10 pm, with the result expected to be announced by Sunday afternoon.
If, as expected, no candidate receives more than 50% of the vote, there will be a run-off election on April 6.
There are no women in the field of nine candidates standing in the election. The incumbent president, Zuzana Čaputová, is not running for a second five-year term despite her continued popularity.
According to opinion polls, there are two clear favourites. Liberal former foreign minister Ivan Korčok promises to be a counterweight to the left-wing nationalist government under Prime Minister Robert Fico.
A liberal Social Democrat, Peter Pellegrini, who is part of the government coalition, is calling on Slovakians to overcome the country's crippling political divide. He wants to maintain a good relationship with the government as well as the opposition.
Slovak politics and society are currently deeply divided, and the climate between the government and opposition has been tainted by mutual accusations.
There is a tense debate about the country's stance on the war in Ukraine, but also about the rule of law and democracy. The country has seen repeated mass protests against the government.
