The CNDP leader stands accused of war crimes committed in the Congolese town of Bukavu, the capital of Sud-Kivu province, which his forces briefly captured in June 2004.
On Friday, Rwandan and Congolese forces engaged the FDLR (Democratic Forces for the Liberation of Rwanda), some of whom took refuge in eastern DR Congo after participating in Rwanda's 1994 genocide, killing nine fighters.
The two armies released a statement on Saturday, confirming the deaths of the FDLR rebels during clashes.
But the FDLR has denied that fighting took place with the joint force, saying that none of its fighters had been killed.
Ignace Murwanashyaka, the FDLR chairman, told the AFP news agency: "This is all a lie. They killed none of our men for the simple reason that there has not been fighting between our troops and this coalition."
"According to reports reaching me from the ground, the Kigali and Kinshasa armies fought with the Mai-Mai ... Nine Congolese soldiers were killed and one wounded in the clashes," Murwanashyaka said, referring to a Congolese rebel group.