"They have been accusing us but wrongly. Rwanda has never intervened in the Congo ever since we left on 5 October 2002," Joseph Mutaboba, the Rwandan president's special envoy to the Great Lakes, told the BBC's Network Africa programme.
Rwanda has twice invaded its much larger neighbour, saying it wants to stop Hutu rebels from operating there.
It claims that two rebel brigades are fighting with the Congolese army.
Mr Kabila has appealed for a multi-national force to help restore order.
The UN Security Council late on Tuesday called for an immediate ceasefire and issued a statement in which it "strongly condemned the offensive operations" against its peacekeepers.
UN forces have been using attack helicopters and tanks to try to stop the rebel advance, but they say the rebels work in small groups, making them difficult to locate and repulse.
Alan Doss, the head of the UN mission in DR Congo (Monuc), told the BBC his forces were stretched to the limit and needed urgent reinforcements.
He said his troops, the largest peacekeeping force in the world, would do their utmost to stop major towns in the region from falling to the Tutsi rebels led by Gen Nkunda.
"We are going to remain there, and we are going to act against any effort to take over a city or major population centre by force," he said from Kinshasa, the Congolese capital.
Rutshuru houses tens of thousands of displaced people and dozens of aid workers are usually based there.
A UN worker said thousands of people were fleeing Rutshuru heading toward the Ugandan border to the north.
Thousands flee Congo fighting
An estimated 20,000 people have already fled towards Goma, many of them having left a refugee camp in Kibumba as the fighting approached on Monday.
About 200,000 people fled their homes after fighting resumed in the area in late August.
Ron Redmond of the UN refugee agency says it almost impossible to reach those in need of help.
"We simply cannot send teams out into the countryside. There's too much fighting going on; it's too dangerous; it's anarchy," he said.
Gen Nkunda says he is fighting to protect the minority Tutsi community from the Hutu militia which carried out the 1994 genocide in Rwanda.
But Alistair Dutton, Christian Aid humanitarian manager for Africa, told the BBC that the fighting was also for control of resources.
Eastern DR Congo is rich in gold and other minerals, such as coltan, used in mobile phones.
A peace deal was signed in Goma between the government and various rebel groups at the end of January.
Although he signed the deal, Gen Nkunda - whose main strongholds are in Kichanga in the Masisi Mountains and Bunagana town bordering Uganda - has always refused to disarm while Rwandan Hutu rebels still operate in the area.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.