About 1.6 million eligible voters were eligible to choose the country's third president since the country gained independence in 1991 as Yugoslavia began to break apart.
The election comes just two months before the country takes over the rotating, six-month European Union presidency.
A run-off has been scheduled for November 11.
Population: 2 million
Size: 20,000 sq km
- Declared independence from Yugoslavia in 1991
- Joined European Union and Nato in 2004
Peterle, 59, is a conservative member of the European Parliament who campaigned as an independent and has the backing of the government of Janez Jansa, the prime minister.
He served as Slovenia's first prime minister in 1992 after the country gained independence from the Yugoslav Federation, and later served as foreign minister.
Peterle billed himself as "The Right Man" for Slovenia - one versed in both domestic and foreign policy - and also sought to appeal to leftist voters.
"We Slovenians can be different, but we should try not to be divided when it comes to important issues," Peterle told The Associated Press earlier on Sunday.
He said if he wins, he would have "co-operative, not competitive" relations with the premier.
Peterle's election would suit Jansa and could help strengthen his shrinking popularity.
Tuerk, 55, was Slovenia's ambassador to the UN and is a former US assistant secretary-general.
Gaspari, also 55, is a former Central Bank governor credited with the country's smooth adoption of the euro currency in January.