The 775 coffins with the remains of newly identified victims from mass graves are being laid to rest at the Potocari cemetery, outside Srebrenica.
More than 7,000 (8372 is the official number, I believe) Muslim men and boys from the town were killed by advancing Bosnian Serb troops in July 1995.
The massacre was the worst atrocity in Europe since World War II.
Serbian President Boris Tadic is attending the ceremony, in what is seen as a significant gesture.
In March, Serbia's parliament passed a landmark resolution apologising for the massacre, saying Belgrade should have done more to prevent the tragedy.
Srebrenica had been declared a UN safe zone, to which thousands of Bosnian Muslims (Bosniaks) had fled during the 1992-95 Bosnian war. But the Bosnian Serb army easily overran the lightly-armed Dutch force there in July 1995.
The massacre is the only episode of the conflict to have been deemed a genocide by the UN tribunal.
Thousands of people are attending the ceremony at the Potocari cemetery - the biggest Srebrenica funeral so far.
New rows have been made for the burial of 775 victims, who will join nearly 4,000 already there.
Mourners mingled among the coffins, looking for the names of loved ones.
Bosnian Security Minister Sadik Ahmetovic told the crowd the international community should help bring fugitive Bosnian Serb wartime military commander Radko Mladic - "the man who brought us our suffering" - to justice.
A statement read out from US President Barack Obama said: "We recognise that there can be no lasting peace without justice."
Mr Tadic, whose attendance brought a mixed response from mourners, said: "With the arrest of General Mladic I would know that part of my job is finished. We need this for the future, for building confidence, for our forthcoming generations."
Speaking at the commemoration, Bosnian Grand Mufti Mustafa Ceric called on European politicians to bring about the Bosnian Muslims' desire to have a "state in Europe that will protect us from the next genocide".
"Civilisation does not begin with the burial of a Bosniak. Civilisation begins with a birth of a Bosniak [not] afraid of the next genocide."
Hasan and Suhra Mahic, both in their 80s, were finally burying their sons Fuad and Suad.
"I would have preferred that all of us have been killed together, then we would not have had to live through this," Hasan told the AFP news agency.
Ramiza Gurdic was burying her son Mehrudin, alongside her husband and another son already in the cemetery.
"How can you forget, how can you forgive? I think about them every day. I go to bed with the pain and I wake up with the sadness."
But many Serbs in the region reject the established narrative of July 1995, the BBC's Mark Lowen in Srebrenica reports.
"The Serb people are portrayed in the media as committing genocide, but it isn't so," Mladen Grujicic, who works for a local association helping the families of Serb victims of the war, told the BBC.
"No Serbs contest that a crime happened in Srebrenica, but they're insulted when the numbers are manipulated," Mr Grujicic says, adding that Serb victims of the war have been forgotten.
Despite attempts to lay the past to rest, Srebrenica remains segregated 15 years after the tragic events, our correspondent says.
UK Prime Minister David Cameron said the atrocity was "a crime that shamed Europe".
My heart goes out to the families and friends of the victims being buried today, those already buried, those still unidentified after 15 years and everyone affected by the genocide, as well as the greater war. Nobody should ever endure suffering like this.