Leaders of the mainly Tutsi RCD-Goma expressed this view as they gathered for talks on Tuesday in their stronghold, Goma, located in the eastern part of the country along the Rwanda border.
Western diplomats in the capital Kinshasa said there was a risk the RCD might pull out of the transitional government, meant to shepherd the country to elections in 2005 after a five-year civil war.
"The process has broken down and we need to repair this break down," Azarius Ruberwa, the head of RCD and one of Congo's four vice-presidents, told United Nations radio.
Ruberwa and other RCD senior officials attended Monday's mass burial of the 160 people shot, hacked and burned to death on Friday night at a refugee camp in western Burundi.
"We need to stop, re-read the [peace] agreement and the conclusions of the negotiations because it is incomprehensible that, during a peace process, genocide of Congolese people takes place abroad," he said.
A Hutu rebel group fighting in Burundi has claimed responsibility for the attack, but the RCD has accused the Congolese army of taking part in the killing.
Both Rwanda and Burundi have
threatened to cross into Congo
Renegade RCD soldiers launched a revolt in eastern Congo in June, saying they wanted to protect Congolese Tutsi - known as Banyamulenge - living in the area.
Both Rwanda and Burundi have said their armies may cross into Congo if the Kinshasa government fails to disarm the Hutu rebels still on its territory, and their allied militia.
"We are worried as we are being threatened by everyone. Rwanda has threatened to attack. Burundi has threatened to attack. Now Ruberwa has threatened to stop taking part in the transition," Kinshasha government spokesman Henri Mova Sakanyi said.
"This is a plan to destabilise the process."
Tiny Rwanda has already invaded Africa's third biggest nation twice - in 1996 and in 1998 - to root out Hutu extremists who fled there after committing the 1994 Rwanda genocide.
Rwanda's second invasion triggered the war which at its height dragged in six African armies. Three million people died, mostly from hunger and disease.
The conflict was declared over last year and a transitional government bringing together President Joseph Kabila and his
former foes was set up.
But progress towards peace has been slow, and the June revolt in the east highlighted the challenges facing the government as it tries to assert its authority across the vast country.