Kuzmanovic, 76, from the powerful Union of Independent Social Democrats (SNSD) has a strong lead over his Serb Democrat Party rival Ognjen Tadic, who has 33% of the votes. There were 10 candidates seeking the presidential post.
"According to votes counted, Rajko Kuzmanovic has 46.55% of the votes," the agency cited the Prime Minister Milorad Dodik as saying.
Kuzmanovic has already thanked his voters promising them, "to be a president of all Republic of Srpska citizens regardless of their nationality or political party. I will represent the republic and protect its unity."
The Central Election Commission said turnout was 40% in the Serb-Bosnian entity which has a population of 1.1 million.
The elections were called following President Milan Jelic's sudden death on September 30. Official results are due by December 24.
The first president to be elected in the republic was Radovan Karadzic in 1992. Karadzic is currently wanted for war crimes by the Hague Tribunal.
