Meanwhile France, which holds the rotating presidency of the EU, said it supported sending forces to the area.
French Foreign Minister Bernard Kouchner said up to 1,500 men could be deployed "in Europe's name within eight to 10 days".
UN spokesman Madnodge Mounoubai, in the capital, Kinshasa, said the UN was not evacuating Goma.
He said civilian personnel were being moved to a base near Lake Kivu, because there were better facilities for the UN staff there including water and food.
On Tuesday night, supporters of renegade General Laurent Nkunda's took the town of Rutshuru, near the Ugandan border.
Neighbouring Rwanda has been accused of backing Gen Nkunda, who left the army and launched his own low-level rebellion after DR Congo's five-year conflict officially ended in 2003.
'Accusing us wrongly'
On Tuesday evening, Mr Kabila sent two envoys to Rwanda to discuss the crisis. But the Rwandan government continues to deny it has anything to do with the conflict.
"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.
Footage of DR Congo government troops, displaced people and UN peacekeepers
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 multinational force to help restore order.
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 has 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.