Victory for the former communist frontrunner in a pack of 14 candidates would give control of the presidency, parliament and government to the same party for the first time since Slovakia's independence in 1993.
Fico, 49, has earned valuable political capital during his six years as premier with an anti-austerity agenda tempered by fiscal discipline.
The economy is set to expand by 2.3 per cent this year, driven by its exports of electronics and cars.
The non-partisan Kiska, 51, with no communist past, came into the vote with 24 per cent backing and is seen as an untainted political novice with a good nose for business.
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The prospect of Fico consolidating his power has galvanised both the political class and voters in the country of 5.4 million, which joined the European Union in 2004 and the eurozone in 2009.
The election has become "a referendum on Robert Fico's government and the concentration of power", Grigorij Meseznikov from the Bratislava-based Institute for Public Affairs told AFP.
Worried about a power grab, long-time Fico supporter Hubert Bystricky, an unemployed 57-year-old, said he voted against him today.
"He's a good politician but I don't want him to have all the power in the country," he told AFP in Bratislava, adding that he chose the "weakest candidate as a gesture of protest".
A Fico win would trigger a reshuffle in the Social Democrat government, but the party would still control a comfortable 83-seat majority in the 150-member parliament until general elections in 2016.