Constantin Charhondangwa, the head of civil society in the Bukavu region, said the parcel of land owned by the ex-rebel was sold to a resident. The new landowner discovered the remains when he dug up the land put in a septic tank, Charhondangwa said.
Bambi and state-run TV said as many as 2,000 people are buried in the twin graves.
U.N. officials visited the site and confirmed the presence of the mass graves but did not offer an estimate of the number of dead.
Madnodje Mounoubai, a spokesman for the U.N. peacekeeping mission in Congo, said the world body is calling for authorities to undertake "a serious investigation."
The discovery comes as eastern Congo has once again come to the brink of war, with a different rebel group fighting government forces.
Bukavu has not been touched by the latest round of violence, but has been a frequent theater of war. It is located 60 miles (100 kilometers) southeast of Goma, the epicenter of the latest fighting.