Friday's Le Monde newspaper has seen what it describes as "an almost definitive version" of a 600-page UN report. The document investigates human rights abuses in eastern DRC, between 1993 and 2003.
Over a million Hutus fled to the DRC in the wake of Rwanda's 1994 genocide, which ended when President Paul Kagame's RPF forces took control of the country.
Le Monde says the report identifies "systematic attacks" against these Hutu refugees by the Rwandan army - and the Congolese rebel group the AFDL - in the years 1996 to 1998.
The report suggests that there could be a basis for a charge of genocide.
Although other armies are also cited in the investigation, the paper claims that Kigali has spent weeks attempting to quash it. Le Monde says that Kagame threatened last month to pull Rwandan troops out of UN peacekeeping missions over the allegations.
The paper also quotes a letter from Rwandan Foreign Minister Louise Mushikiwabo, written earlier this month to the UN. Her letter suggests similar consequences if the report is "published" or "leaked to the press".
But Le Monde says Ban Ki Moon is uneasy with any use of the term "genocide" in the final version of the report, due out next month - and that he has warned its authors to verify the legal basis of any accusations they make.
Rwanda meanwhile described the allegations against its army as "outrageous".