During several days of fighting Tutsi rebels under the leadership of Gen Laurent Nkunda have advanced to just outside Goma, where they have paused and declared a ceasefire.
Gen Nkunda has told the BBC the goal of his forces was to protect his Tutsi community from attack by Rwandan Hutu rebels, some of whom are accused of taking part in the 1994 genocide.
But many in DR Congo say that Rwanda supports Gen Nkunda's forces - something Rwanda denies.
Correspondents say that a race for the area's mineral wealth is fuelling the conflict as much as ethnic enmities.
Diplomats are using the current pause in hostilities to try to resolve the situation.
EU foreign policy chief Javier Solana has spoken to Rwandan President Paul Kagame, and EU Aid Commissioner Louis Michel has met Congolese President Joseph Kabila in an attempt to bring the two leaders together.
The foreign minister of Rwanda is visiting Kinshasa, where US Assistant Secretary of State for African Affairs Jendayi Frazer is expected to arrive.
Ms Frazer said on Wednesday that she had no evidence that Rwandan troops were on Congolese soil, but that she believed Gen Nkunda's rebels were using Rwanda as a safe haven.
Tens of thousands of civilians have fled towards Goma as the rebels have advanced on the city.
Aid agencies have said they are unable to work in the climate of violence and many people are without food, shelter or clean water.
The UN children's agency, Unicef, said the latest bout of fighting had resulted in a "very bad" humanitarian situation.
"We're talking tens of thousands of people who have fled towards Goma and thousands more who are fleeing north to a town called Kane Byunga," Unicef's Jaya Murthy told the BBC's World Today programme.
"Many of the population that have fled are staying in vacant schools, in churches and outside."
On Thursday Gen Nkunda said he was opening a "humanitarian corridor" so that aid could reach the thousands of people trapped between his forces and UN soldiers backing up government troops.
Fears are growing for the welfare of 39 wildlife rangers who were reportedly forced to flee into dense forest after their headquarters in eastern DR Congo were stormed by rebels on Sunday.
Rangers in Virunga protect some 200 of the world's last mountain gorillas
The rangers, who protect some of the world's last mountain gorillas in Virunga National Park in North Kivu province, are reported to have no food, water or shelter.
"Virunga is in an unprecedented crisis," said Dr Emmanuel de Merode, provincial director of the Congolese Institute for Nature Conservation (ICCN).
"The fighting continues to spread in all directions, the rangers have lost control of the southern sector of the park... We urgently need support to protect the rangers and their families."
Bernard Kouchner, the French foreign minister, said a potential European force of as many as 1,500 soldiers could provide humanitarian assistance in Goma but would not fight the rebels.
He said the EU security committee would meet in Brussels to discuss the idea.
Retreating Congolese troops were blamed for causing chaos in the city of Goma, which was calm but tense early on Thursday after a night of gunfire and looting.
There are reports that several people were killed.
Correspondents say the 17,000-strong UN force in DR Congo - the world's largest - is stretched to breaking point.
The UN Security Council took no action on a request from the country's mission head, Alan Doss, for temporary reinforcements but said some of its peacekeepers could be redeployed from elsewhere in DR Congo to back up those in Goma.
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