The killing took place in Mutarule, about 50 kilometres (30 miles) south of Bukavu, a local official told AFP by telephone from the capital of Sud-Kivu province.
The sources said the victims were ethnic Bafuliru, and most of them were killed while sleeping in a Protestant church after taking part in a parish meeting.
The victims were either shot or stabbed to death.
In all, "eight men, 14 women, 10 children and a soldier" were killed, said one local councillor, reporting 33 deaths. He added that 28 more people were wounded.
The UN mission in DR Congo (MONUSCO) late Saturday issued a statement saying that "fierce fighting" had taken place the night before between the Bafuliru on one side and the ethnic Barundi and Banyamulenge on the other.
"This violence is unacceptable and must end immediately," said Martin Kobler, head of MONUSCO.
The Barundi and Banyamulenge are Tutsis originally from Burundi who have been living in Sud-Kivu for generations.
There has been a conflict for a dozen years between the Bafuliru and the Barundi over property and custom issues.
South Kivu's Interior Minister Jean-Julien Miruho told AFP that the attack was likely in revenge for cattle raids in the region.
"It is a problem of (stolen) cattle, and one side went to seek revenge," he said.
Local sources also confirmed that there had been a problem of stolen cattle in the region.
UN peacekeepers have been sent to Mutarule to evacuate the wounded and help the local authorities and the Congolese army restore calm to the area.