Bosnian Serb president Dragan Cavic has called the massacre of thousands of Bosnian Muslims at Srebrenica a black page in the history of the Serb people.
Some politicians have questioned whether the crime took place
In a special TV broadcast he said he understood the pain of the relatives of those who died in the incident.
The BBC's Sarajevo correspondent says it is the closest any senior Serb official has come to an apology for the killings, carried out by Serb forces.
More than 7,000 Bosnian Muslim men and boys were killed at Srebrenica in 1995.
The massacre occurred after Serb forces stormed a UN designated safe area.
Two weeks ago a special Bosnian Serb commission investigating the incident made the first admission that Serb forces had taken part in the killings.
The BBC's Nick Hawton in Sarajevo says the statement from Mr Cavic is unprecedented and mark a watershed in Bosnian Serb politics.
In it he said those Serbs who had carried out the killings at Srebrenica had committed a crime against their own people and that those days in July 1995, when the massacre took place, represented a black page in the history of the Serb people.
Until now, Bosnian Serb politicians have never acknowledged the scale of the crime and some have even questioned whether a crime had taken place.
Mr Cavic's statement is also significant because he comes from the same political party as the former Bosnian Serb wartime leader Radovan Karadzic, who is wanted by the war crimes tribunal in The Hague to face genocide charges over what happened at Srebrenica.
But our correspondent says nothing less than a full apology for Srebrenica is likely to be accepted by Bosnia's Muslim community.