The Gendarmerie unit was presented for top Bosnian Serb leaders in Banja Luka, the main city in the Bosnian Serb-run part of the country.
Bosnian Serb politicians say the unit is part of police regrouping and modernization, but the country's Bosniaks warned it could speak fear among other ethnic groups amid memories of the 1992-95 conflict that left 100,000 people dead.
Postwar Bosnia consists of a Serb part and a part run by Bosniaks, who are mainly Muslims, and Croats. The two entities are kept together by joint Bosnian institutions, including state-level security agencies.
The leading Bosnian Serb politician Milorad Dodik, who is the Serb member of Bosnia's multi-ethnic presidency, said the new police unit was designed like similar units in the West.
"We are organizing ourselves in a new way," Dodik said. "Republika Srpska is sending the message that we want stability and peace, as a priority, but at the same time we are ready to tackle all the challenges which could eventually arise from any side, challenges which include any threat to constitutional order of Republika Srpska or threat to security for any citizen."
Serbs, who took up arms in 1995 to carve out a state in Bosnia after the country split from the former Yugoslavia, have insisted on maximum independence from the central government. Dodik has repeatedly called for the Serbs to separate from the rest of Bosnia.
In Sarajevo, the interior minister of the second Bosnian entity, the Federation of Bosnia-Herzegovina, Aljosa Campara, warned that the parading of the Serb unit creates unease among Bosniaks and Croats living in the Serb-run entity.
"I don't think this display means much ... but it can mean, yet again, heating up of the atmosphere, destabilization of human relations, creation of fear," he said, adding it is "nothing that citizens of Bosnia need."