The crowd marched through the ethnically divided southern town of Mostar holding banners reading "Not my president" and "RIP democracy" to protest Zeljko Komsic's victory.
Bosnia's presidency also has a Muslim and a Serb member. A peace deal that ended Bosnia's 1992-95 ethnic war created a Muslim-Croat region and a Serb region held together in a central government.
Komsic advocates strengthening Bosnia's unity. Nationalist are disputing his win in an election Sunday, saying he was backed by Muslim voters and does not represent Croats.
Persisting ethnic divisions in Bosnia have held the country back from advancing toward EU and NATO membership since the war.
The protesters in Mostar also lit candles outside the local office of the Croat presidency. The office was established by Komsic's predecessor, Dragan Covic, the Croatian Democratic Union party candidate who lost Sunday's vote.
Covic has called for the formation of a third, Croat, entity in Bosnia, which would mean further division of the country along ethnic lines.
Some Bosnian Croat-dominated municipalities have declared Komsic unwelcome in their communities. The dispute could trigger a post-election crisis.
"How is he going to represent the interests of the Croat people if he was not elected by those who should have (elected him)?" retired professor Frano Dubic, 65, said. "There can't be stability in a multi-ethnic community if one of the nationalities living there does not have equal rights. Unfortunately this is what is happening here."
Komsic's election also has been criticized in neighboring Croatia.
"We are again in a situation where members of one constituent people ... are electing a representative of another, the Croat people," Prime Minister Andrej Plenkovic said earlier this week
A bid by nationalists to carve Bosnia along ethnic lines was at the core of the 1990s' conflict that killed 100,000 people and left millions homeless.
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