In New York, UN Secretary-General Ban Ki-moon named former Nigerian President Olusegun Obasanjo as his special envoy to help resolve the crisis.
Mr Ban added that he was willing to meet Mr Kabila and Mr Kagame soon.
Meanwhile an aid convoy escorted by UN troops arrived in Rutshuru, a rebel-held town 75km (45 miles) north of Goma.
It carried medical supplies and water purification tablets. The UN said it hoped food convoys could follow.
Aid workers found that refugee camps that had held tens of thousands are now virtually empty.
It is believed many people left fearing further violence.
While as many as 50,000 displaced people reached Goma, many others have tried to return to their homes on foot through rebel-held territory.
Many have been reduced to foraging for wild roots and berries in the bush, without safe shelter, water and care.
The recent rebel offensive was exacerbated by a wave of killing, looting and raping by retreating Congolese soldiers.
Brown's pledge
The Congolese government accuses Rwanda of backing the rebels, but both countries' presidents have agreed to attend a regional summit on the situation.
UK Prime Minister Gordon Brown has said the international community must "not allow Congo to become another Rwanda".
In 1994, 800,000 people died in Rwanda's genocide, which is seen as the origin of the current conflict across the border.
Gen Nkunda says he is fighting to protect his Tutsi community from attack by Rwandan Hutu rebels, some of whom are accused of taking part in the genocide.
There have been accusations of collusion between DR Congo's army and Hutu guerrillas.
The Congolese government, for its part, has accused Rwanda of backing Gen Nkunda.
Rwanda denies this, but it has twice invaded its much larger neighbour in recent years.
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