A third child is still missing. The three, aged nine, 11 and 12, drowned on 17 March after reportedly being pushed by Serbs into the Ibar river that separates the divided town of Kovoska Mitrovica in northern Kosovo.
But the head of the United Nations police force in the southern Serbian region said on Saturday that investigators in Kosovo had not been able to confirm the allegations.
The funerals, originally planned for Friday, were postponed until Sunday because of high tensions.
Last week Kosovo experienced the bloodiest communal riots since the end of the war there five years ago. A total of 28 people have been killed so far and more than 600 injured.
Calling for calm
Kosovo's ethnic Albanian prime minister, Bajram Rexhepi, has
called for calm during the funerals. "The ceremony must be dignified and organisers must take care that their speeches do not foment new tensions," Rexhepi said.
The families of the children have also urged the ethnic Albanian majority not to exploit the tragedy.
The prime minister said he would attend the funerals, along with several ministers and representatives of the international
The bodies of the two Albanian children were washed at the Hadzi Veseli mosque in southern Kosovska Mitrovica on Sunday morning and laid out in coffins before being transferred to the village of Cabra. Kosovo's Albanian majority is mainly Muslim.
"Serbs killed our boy. But we will leave it up to the law and the local authorities to take care of it for now," said Sali Deliu, the uncle of one of the dead boys, Egion Deliu.
Youths throw stones at police
during protests in Belgrade
"We will not take revenge. We are sorry for all those who have been killed because of our children."
Another of the boy's relatives, 29-year-old Adem Deliu, said: "I feel bad but I can't do anything because of the situation."
Asked whether co-existence between Kosovo's Albanian and Serb communities would be possible in future, he said: "For us (Albanians) history has been difficult and we have always had victims. But we never thought we would see that happening with KFOR and the UN here."
KFOR is the NATO-led peacekeeping force in the Kosovo. Both Serbs and Albanians have been accusing NATO peacekeepers of not doing enough to prevent violence in the past few days.
A tense calm prevailed in Kosovo on Sunday, with NATO peacekeepers and UN police strictly manning the road between Kosovska Mitrovica and the provincial capital Pristina.
About 2000 NATO reinforcements are being deployed there to
support the 17,000 KFOR troops and the 10,000 UN and local police. The extra soldiers are being sent from Britain, France, Germany and have orders to use force if fired on.
"Serbs killed our boy. But we will leave it up to the law and the local authorities to take care of it for now. We will not take revenge. We are sorry for all those who have been killed because of our children."
Sali Deliu, the uncle of one of the dead boys
Late on Saturday, more than 7000 people took to the streets of towns across neighbouring Montenegro to protest at last week's clashes.
Rallies were also held overnight in the Adriatic town of Bar and the eastern town of Bijelo Polje against the riots in Kosovo, a UN-administered province of the loose union known as Serbia and Montenegro that was created from the former Yugoslavia.
Protesters led by Christian Orthodox church dignitaries and opposition heads marched through the Montenegrin capital Podgorica, waved Serbia-Montenegro and Orthodox flags and chanting: "Serbia, Serbia!", "Kosovo is the heart of Montenegro, the heart of Serbia!".
The government of Montenegro has decreed Sunday a day of mourning for the victims of the violence.
Belgrade has also decreed a day of mourning in response to what it called "the pogrom of the Serbs and the destruction of Serb sanctuaries and homes in Kosovo".