The head of the election commission, Vehid Sehic, told reporters in Sarajevo that data collected in 111 municipalities show that a total of 46.46 percent of eligible voters went to the polls.
This year's turnout is the lowest since the signing of the Dayton Accord.
Bosnians chose councillors and for the first time directly elected mayors in 140 municipalities in the country's autonomous
Muslim-Croat and Serb halves. They also voted in the neutral northern Brcko district.
According to information available on Sunday morning, the Social Democratic Party (SDP), led by Zlatko Lagumdzija, and the Party of Independent Social Democrats (SNSD). led by Milorad Dodik, managed to remain at their positions in the majority of the municipalities in which they were in power and gained a surprisingly large support in some parts of Bosnia known as the strongholds of the Muslim Party of Democratic Action (SDA) and the Serb Democratic PArty (SDS).
Lagumdzija told a news conference in Sarajevo in the night between Saturday and Sunday that his party remained in power in Sarajevo's most important municipalities -- te Centre, and New Sarajevo -- and added that the SDP candidate also won the post of the head of the Novi Grad municipality,
The SDP also won in Bihac, previously ruled by the SDA.
SDP Secretary General Karlo Filipovic told Hina the party also marked a great success at the elections for the first assembly of the Brcko District.
"We have entirely realised our election objective," SDP president Lagumdzija told reporters.
SNSD secretary general Igor Radojicic told reporters his party most definitely defeated the SDS in Banja Luka
The president of the Croatian Democratic Union of Bosnia-Herzegovina (HDZ BiH), Barisa Colak, told reporters in the southern Bosnian town of Mostar that his party would remain in power in parts of Bosnia mostly populated by Croats. He expressed satisfaction with the election results.
In spite of expectations that the integral results of the local vote would be announced in the night between Saturday and Sunday, the election commission presented preliminary and incomplete results for only 20 of 140 municipalities and towns.
Statements by representatives of leading political parties are confusing because they all claim they won.
The election commission said it would announce new election results around 22.00 hours Sunday.