About 6,000 polling stations opened at 7:00 am (0600 GMT) for the more than four million eligible voters.
The latest polls showed outgoing President Ivan Gasparovic, 67, comfortably ahead with a support exceeding 50 percent -- while opposition candidate Radicova, 52, was given 30 percent.
But the final result depends on the turnout: if none of the candidates obtains more than 50 percent of all eligible votes in the first round, the winner will result from the second round set for April 4.
Source: FOCUS Information Agency