The military intelligence chiefs of neighbouring Rwanda and Burundi have agreed in a rare face-to-face meeting to restore security at their border following years of hostility.

Their commitment to address long-standing insecurity along the shared frontier was made Wednesday during the first public meeting in five years between senior officials from the East African nations.

The sit-down, at the Rwandan border district of Bugesera, was brokered by the International Conference of the Great Lakes Region (ICGLR) to which Rwanda and Burundi belong.

The regional bloc called the meeting to address "persistent insecurity on the common border" and the "many unfortunate incidents that have occurred there recently", said Colonel Leon Mahoungou, the ICGLR mediator for the talks.

"I am pleased with the results you have achieved at the end of your exchange," he said in a statement.

"I also note with great satisfaction that the meeting resulted in your commitment to work for the return of security on your common borders."

Tensions between Rwanda and Burundi have festered for five years, marked by deep mutual distrust and sporadic violent clashes involving armed groups along the border.

Burundi has accused its neighbour of arming and training rebel groups hostile to the regime of late President Pierre Nkurunziza, whose candidacy for a third term in 2015 plunged the country into a violent political crisis.

Nkurunziza died on June 8, officially of cardiac arrest.

Evariste Ndayishimiye, a former general and high-profile ruling party cadre, was elected president on May 20 and took office on June 18.

Rwanda, for its part, has accused Burundi of sheltering armed rebels hostile to President Paul Kagame that are allegedly responsible for cross-border attacks on Rwandan security forces.

The chiefs of staff of the armies of Rwanda and Burundi made informal contact after Ndayishimiye's election, a senior Burundian military official told AFP on condition of anonymity.

Kagame had extended an olive branch to the new Burundian leader, expressing hope that direct talks could resume between the old foes.

Ndayishimiye has sent conflicting signals, though he has said he is ready to live in harmony with all Burundi's neighbours.

On Thursday, Rwanda began repatriating some 500 Burundian refugees, an operation administered by the United Nations refugee agency UNHCR.

The goodwill gesture came following a request from Burundian authorities.