An estimated 250,000 people have now fled the fighting between rebel forces of Gen Laurent Nkunda and pro-government militias.
Gen Nkunda says he is fighting to protect his Tutsi community from attacks by Rwandan Hutu rebels, who fled to Congo after the 1994 genocide.
The UN mission in DR Congo, Monuc, said on Sunday that a new front had opened up in the conflict.
Fighting was reported near Ngungu, 60km (37 miles) to the west of Goma.
A UN spokesman said thousands of civilians had fled to a peacekeeping base to escape the fighting but that it was not clear how the clashes had started.
Previously, fighting had been largely to the north of Goma, where Gen Nkunda halted his advance 10 days ago
Correspondents say the fighting has raised fears that the rebels could be trying to encircle the city.
African forces
African leaders have called for an immediate ceasefire and for UN peacekeepers to get greater powers.
At a summit in Nairobi on Friday, leaders from seven countries said the peacekeepers' mandate should be amended to give them "peace-making" capabilities.
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They also said rebel groups in the region should be disarmed according to existing agreements and said humanitarian corridors should be set up to help the displaced.
The Southern African Development Community (SADC) has also called for a ceasefire and said it may consider deploying peacekeeping troops.
"SADC will not stand by and witness any destructive acts of violence by any armed groups and if necessary will send peacekeeping forces," the group said in a statement from Johannesburg.
The UN has 17,000 peacekeepers in DR Congo, making Monuc its largest mission in the world.
But only a few hundred peacekeepers are in the areas affected by the latest violence, and human rights groups have also criticised the UN for failing to prevent the killings.
The UN has accused both sides of war crimes, following the reported killing of several civilians in the eastern town of Kiwanja this week.
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