The attack came as tensions rise days ahead of a constitutional referendum on May 17 which could allow Nkurunziza to stay in power for 16 more years.
The government has in recent weeks deployed soldiers to border areas after accusing exiled opposition groups of seeking to disrupt the vote.
They said a group, armed with guns and knives, killed dozens of people and also set fire to buildings.
"These criminals went house to house and committed real carnage," said a local official speaking on condition of anonymity. He said he was "horrified" by the violence.
"Some of the victims were stabbed, others were shot, there is even a whole family that was burned alive in their home." The perpetrators and their motive are not yet known but local residents said the attackers crossed into DR Congo after carrying out the raid.
"For now, these criminals have not been identified, but an investigation is underway to determine their identity," said a police officer, who did not want to be named.
Nkurunziza, 54, has ruled the tiny central African nation since 2005. His run for a controversial third term in 2015 triggered a deep political crisis that has seen 1,200 people killed and 400,000 flee their homes.
The violence and abuses are being investigated by the International Criminal Court (ICC) while a vicious press crackdown has seen the majority of independent journalists leave the country.
The vote is taking place in tightly-controlled conditions, and parties which advise electors to abstain - rather than cast a Yes or No ballot - risk up to three years' jail.
Earlier this month Burundi's press regulator suspended broadcasts by the BBC and Voice of America (VOA) and warned other radio stations, including Radio France International (RFI), against spreading "tendentious and misleading" information.
Burundi's exiled opposition, gathered in an alliance called CNARED, has called for a boycott of the referendum, which it describes as the "death knell" to a 2000 agreement that helped end a bloody civil war.
But if the amendment is approved, Nkurunziza would be entitled to stand for two more seven-year terms from 2020.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)