Mbarushimana said: "The FDLR raises serious questions on the real motives that led the high authority of the UN to rush to incriminate them before even carrying out a preliminary inquiry into these odious acts."
The group urged the UN to "set up without delay an independent international commission tasked with shedding full light on all these criminal acts", saying it was ready to "collaborate with this commission" with Khare.
Speaking to Al Jazeera, Guy Momat, a Congolese journalist, criticised the UN Organisation Stabilisation Mission in DR Congo (Monusco), which has a base less than 20km from Luvungi.
"This is not the first [such incident], do you remember in 2008, in November, there, 150 Congolese [were] killed in Kiwanja province, and it was just a mile away from the Monusco camp," he said.
"The Monusco is there, it is a big force, but if you see the situation on the field, we can say this is a failure, nothing happened, people, civilian people, are not protected and they [Monusco] don't have a proper mandate."
Roger Meece, the senior UN envoy in the DR Congo, said on Wednesday peacekeepers did not learn about the rapes for nearly two weeks because villagers had not informed the two patrols in the area.
Meece announced plans to improve communications and prevent any recurrence of sexual violence in the country's east.
One proposal, Meece said, was to have villages report to the UN's forward operating base at Kibua every day.
The US, meanwhile, has offered to back any effort in the fight against sexual violence in DR Congo.
In a statement on Wednesday, Hillary Clinton, the US secretary of state, said her country will help any effort to bring to justice rebels accused in the mass rapes.
She said it was now time for member nations to go beyond that with specific steps to protect civilians against sexual violence and prosecute those who commit such atrocities.
"This horrific attack is yet another example of how sexual violence undermines efforts to achieve and maintain stability in areas torn by conflict but striving for peace," Clinton said.
"The United States will do everything we can to work with the UN and the DRC government to hold the perpetrators of these acts accountable, and to create a safe environment for women, girls, and all civilians living in the eastern Congo."
The UN last year adopted a resolution recognising the importance of preventing and responding to sexual violence as a tactic of war against civilians.