Security Minister Alain Guillaume Bunyoni described the attackers as "terrorists coming from and returning to Congo shot and burned: 26 dead and seven wounded".
Witnesses described to the AFP news agency hours of violence that began late on Friday night.
"These criminals went house to house and committed real carnage," one local official said. "Some of the victims were stabbed, others were shot, there is even a whole family that was burned alive in their home."
It is not known who carried out the attacks, but suspicion has fallen on exiled opposition groups who are based on the other side of Burundi's borders. They have vowed to disrupt the 17 May referendum.
Critics say a cult of personality is developing around Mr Nkurunziza, a former Hutu rebel leader who became the first president to be chosen in democratic elections since the start of Burundi's civil war in 1994.