The head of Burundi's army has accused Congolese troops of taking part in the massacre of more than 150 Tutsi refugees last Friday.
Many of those killed were women and children
Brigadier-General Germain Niyoyankana warned that if the Congolese government did not act, Burundi could send troops into Democratic Republic of Congo.
A Burundi rebel group has admitted responsibility for the slaughter and denied that other groups were involved.
The massacre has raised fears of worse conflict across central Africa.
Many of the victims were Tutsi women, children and babies, who fled eastern DR Congo in June after fighting between Tutsi rebels and the army.
"There is no longer any doubt that the site at Gatumba was the target of a coalition... of negative forces made up of the [Burundi Hutu rebel National Liberation Forces] FNL, acting as guides, former Rwandan armed forces and part of the DRC army," said General Niyoyankana.
"I have not ruled out an offensive against the DRC aimed at making them respect our country's borders," he said.
Rwanda has also warned that it could send its soldiers into DR Congo to prevent another genocide.
DR Congo's Defence Minister Jean-Pierre Ondekane said that invading his country would not solve the problem "because these rebels are in all three countries," reports the AP news agency.
The conflicts in DR Congo, Burundi and Rwanda are closely interlinked, with DR Congo-based Hutu rebels fighting Tutsi-dominated armies in both Burundi and Rwanda.
Burundi was one of at least six countries with troops involved in DR Congo's five-year civil war, which formally ended in 2002.
More than 150 refugees who had been shot or hacked to death with machetes, were buried in a mass grave on Monday.
Earlier, the United Nations said it had suspended negotiations with the FNL - the only rebel group to remain outside the peace process in Burundi - after it admitted responsibility for the massacre.
Other Burundi rebel groups have agreed a power-sharing deal with the government, under which Hutu Domitien Ndayizeye replaced Tutsi Pierre Buyoya as president last year.
But the FNL says it will only talk to the Tutsi-dominated army, which it says still holds real power.
It admitted responsibility for the massacre but a survivor told BBC News Online that he heard the killers talking languages from DR Congo and Rwanda, as well as Burundi.
Following the massacre, the Burundi government has agreed to long-standing UN requests to move refugee camps away from the DR Congo border.
The Gatumba camp where the refugees were slaughtered was right on the border, across which the killers crossed.
"Burundi has agreed to give us a site for a camp farther away from the border area. In the meantime, the massacre has taken place. There is no way to bring back the lives of those who were killed," said UN spokesman Fred Eckhard.
At the funeral attended by thousands of people, the coffins were laid side by side in a huge common grave, measuring 20m wide by 25m deep.
A banner next to the grave read: "The genocide of Tutsis is a reality".
Some 300,000 people have died in 11 years of conflict in Burundi but until this massacre, the scale of violence had reduced in recent months.