Polling stations opened at 7:00 am (0600 GMT) and will close at 10:00 pm with no exit poll and final results expected around midnight.
In the first round of voting on March 15, Social Democrat Fico captured 28 percent finishing narrowly ahead of centrist Kiska, who scored 24 percent.
Round two is expected to be very close, as the prospect of Fico and his Smer-Social Democrats winning control of both parliament and the presidency has galvanised opponents in the country of 5.4 million, which joined the European Union in 2004 and the eurozone in 2009.
"Kiska has a higher potential to mobilise voters who backed other candidates in round one, as well as so-called protest voters who would not back any partisan, while Fico only has the potential to mobilise Smer," Bratislava-based analyst Grigorij Meseznikov said.
An ex-Communist, Fico wound down his campaign by wooing voters with references to his traditional Catholic upbringing, all the while painting Kiska as a Scientologist, a claim the tycoon flatly denies.
Over 60 percent of Slovaks identified themselves as Roman Catholic in the 2011 census.
"Fico is trying to stir negative emotion by painting Kiska as an alien element in Slovakia's conservative, relatively homogeneous society," Meseznikov told AFP.
Endorsed by heavyweight European Socialists like French President Francois Hollande and European Parliament chief Martin Schulz, veteran leftist Fico, 49, has also tried to cast Kiska as politically naive and out of his depth.
A non-partisan centrist with no Communist past, he is seen as having a nose for business and being incorruptible due to the fact that he has given much of his self-made fortune to charity.
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