Security has been stepped up along the border near the camp
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More than 150 refugees, many of them children, have been buried in mass graves in Burundi.
A local official said the bodies would eventually be sent back to Democratic Republic of Congo for reburial.
The refugees, mostly Congolese ethnic Tutsis, were allegedly killed by armed men from Burundi, DR Congo and Rwanda.
Burundian Hutu rebels have claimed responsibility but a Rwandan group has denied taking part. The DR Congo - Burundi border has been closed.
All three countries have been hit by conflict since Rwanda's 1994 genocide.
The coffins were laid side by side in a huge common grave, measuring 20 metres wide by 25 metres deep, dug by bulldozers in a field belonging to the Burundian army, reports the AFP news agency.
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A banner held next to the grave read: "The genocide of Tutsis is a reality".
Other placards read: "Onub go home," referring to the UN's peace-keeping mission of some 2,000 troops, which failed to prevent the massacre.
Among the crowd of several thousand people at the multi-denominational religious service were Burundi's President Domitien Ndayizeye, a senior Rwandan envoy and DR Congo's Vice-President Azarias Ruberwa - himself a Congolese Tutsi.
A BBC correspondent says the killings have raised tensions in the region - Rwanda has warned that it will take unilateral action if necessary to disarm the Hutu militia group it believes was behind the attack.
Hutu extremists
In an emergency session on Sunday, the UN Security Council condemned with "utmost firmness" the killing
and called on Burundi and Congolese authorities to co-operate to bring those responsible to justice.
The UN has asked Burundi to set up a refugee camp away from the DR Congo border where the killings took place.
The Burundi army has increased security along the normally busy border, it says.
UN Secretary-General Kofi Annan said the incident had "shocked and outraged" him.
Many of the victims were Tutsi women, children and babies, who fled southern DR Congo in June after fighting between Tutsi rebels and the army.
Armed with machetes, guns and grenades, the attackers entered the camp some 10km from the Burundi capital, Bujumbura on Friday evening and set fire to several shelters where they were living.
Ceasefire urged
The president of Burundi said the massacre was carried out by Congolese who had crossed into his country.
But a Burundi rebel group - the National Liberation Front (FNL) - said the killings had occurred during its attack on an army base next to the refugee camp and Congolese and Rwandan fighters were not involved.
FNL spokesman Pasteur Habimana said the camp had been used as a launch pad for attacks against his men by Tutsi groups.
The FNL is the only active rebel group of Hutus fighting against the Burundian government dominated by the Tutsi minority. About 300,000 people have been killed during the 11-year conflict.
Rwanda has also blamed the massacre on Hutu extremists in the DR Congo - some from the militias that carried out the Rwandan genocide of some 800 000 Tutsis and moderate Hutus.
The Gatumba camp where the refugees were residing provides shelter for 1,700 people.
The FNL rebel group said it had aimed to hit a military base, some 500m from the Gatumba camp.
A statement issued by the 25-nation EU urged the FNL to enter peace talks.
"This bloody attack indicates once again that it is necessary for all parties involved in the conflict in Burundi to intensify their efforts, without hesitation, in order to reach real and enduring peace," the statement said.
"An immediate ceasefire between the FNL and the government is the first step in this direction."
In the past, the FNL said it would only negotiate with the Tutsi leadership of the army who, it claims, hold the real power in Burundi.
The rebels have found themselves increasingly isolated since the power-sharing agreement late last year between the government and the larger Hutu rebel group, the Forces for Defence of Democracy (FDD).