Burundi wants 19 combatants who were arrested in Rwanda deported, a demand that could test the fragile relations between the two neighbours.
Rwanda says the Burundian combatants, who identified themselves as members of the Red Tabara - an armed rebel group - were apprehended in Nyungwe Forest on September 29.
According to the Rwanda Defence Force (RDF), the incident was reported to the Expanded Joint Verification Mechanism (EJVM), a regional conflict monitoring team under the International Conference on the Great Lakes Region (ICGLR), to investigate the occurrence.
On Sunday, Burundi released a statement demanding the extradition of the "group of armed bandits", claiming the militants use Rwanda as a hiding base to commit crimes in Burundi.
"A group of armed bandits from Rwimbogo sector in Rwanda attacked two households and killed a 30-year-old man in Kayanza Province in Burundi.
"In pursuit by law enforcement, the group retreated to the hill from where they had come from in Rwanda, taking with them seven goats stolen from the attacked households," Burundi said in the statement without revealing when the attack took place.
Burundi now wants Rwanda to "return to Burundi those [suspected] criminals it has apprehended directly, without passing through other mechanisms."
Bujumbura said it is seeking reciprocity as it has "always done in cases when Rwandan criminals are arrested in Burundi, so that they may be held accountable to justice."
Burundi added: "The government once again condemns this heinous act and welcomes the results of the exchange of information with the Rwandan local security forces, at the request of the Burundian security forces, which have made it possible to locate and track the movements of these criminals in their places of withdrawal."
On Monday, officials from the regional military framework EJVM visited Nyaruguru District in Rwanda, where the group is being detained, and were briefed on the arrest by the RDF area commander, Major Alex Nkuranga.
Rwanda and Burundi have over the years traded accusations related to supporting rebels opposed to their governments.
But in a move aimed at quelling tensions, military officials from both countries met publicly in August, for the first time in five years, to find common ground on the longstanding tensions that have affected security, trade, and movement.
At the meeting, convened by ICGLR, the two countries negotiated a path towards enforcing security at their common border, although no pact was signed.
Following the meeting, Burundian refugees have been voluntarily returning home with the United Nations refugee agency UNHCR saying more are registering to be repatriated after witnessing a return to peace at home.