* Philanthropist Kiska draws support from centre-right
* Many voters don't want PM Fico's party to win more power
* Polling ends Saturday evening, results due overnight (Adds Fico, reports of turnout, changes dateline)
By Jiri Skacel and Jan Lopatka
BRATISLAVA, March 29 (Reuters) - Slovak voters turned out in unexpectedly higher numbers on Saturday for the runoff in the country's presidential election where an underdog philanthropist is challenging political heavyweight Prime Minister Robert Fico.
Polling stations around the country reported a stronger early turnout than in the initial round two weeks ago, when only 43 percent of voters participated and gave only lukewarm support for Fico. But analysts say a higher turnout could help him.
Bookmakers are giving the edge to political newcomer Andrej Kiska, a businessman turned philanthropist riding on the wave of anti-Fico sentiment among right-wing voters as well as distrust in mainstream political parties because of graft scandals.
Fico's disappointing performance in the first round seemed to reflect fear the 49-year-old would amass too much power, which some see as unhealthy for democratic checks and balances.
A Fico victory would give his centre-left Smer party full control of all the main power centres in the euro zone country of 5.5 million, even if the Slovak constitution does not grant the president himself a huge political role.
Fico, who has led the country since sweeping a parliamentary election in 2012, won 28 percent of the vote to Kiska's 24 percent in the first round, a smaller margin than opinion polls had indicated.
Illustrating the uncertainty over the result, Fico said he would go "bite his nails" while awaiting the ballot count at his party's headquarters in Bratislava, news website SME reported.
Polling stations close at 10 pm (2100 GMT) and final results are expected within several hours afterwards.
The president has the power to name or approve some of the main figures in the country's prosecution and judicial branches, and this right has led to political clashes in the past.
CAMPAIGN FOR CHANGE
Rule of law is a key concern for Slovaks as well as foreign investors, the source of economic growth in the past decade.
Slovakia has lured big foreign manufacturers such as car makers Kia and Volkswagen, which have helped keep growth at decent levels even as others in central Europe slipped into recession amid the euro zone crisis.
Kiska, 51, has campaigned on the argument that Slovakia needs a counterweight to Fico's Smer party, which has one-party cabinet rule and controls the majority in parliament.
"Smer" is the Slovak word for "direction" and the party's political orientation is basically social democratic.
"If the president is to represent people, he cannot be the extended hand of a political party," Kiska, an independent who has no party of his own, said in the final television debate earlier this week.
The candidates are close on Slovakia's foreign policy, which keeps the country firmly in the EU's pro-integration camp.
Fico would have to give up his post of prime minister if he wins, but his party would replace him with a Smer nominee. A possible choice to succeed him is Robert Kalinak, the interior minister and longtime member of the party that Fico founded.
Fico, 49, took Slovakia into the euro zone in 2009 and has kept the country friendly to investors despite levying extra taxes on banks and utilities. (Reporting by Jan Lopatka; Editing by Tom Heneghan)