Peacekeepers had retreated to within 3 miles of the city, abandoning positions north of Goma.
The conflict is fueled by festering ethnic hatred left over from Rwanda's 1994 genocide and Congo's unrelenting civil wars.
Nkunda claims the Congolese government has not protected ethnic Tutsis from the Rwandan Hutu militia that escaped to Congo after helping slaughter a half million Rwandan Tutsis.
All sides also are believed to fund fighters by illegally mining Congo's vast mineral riches, giving them no financial interest in stopping the fighting.
Ordinary people are bearing the brunt of the dispute.
"We've had nothing to eat for three days," Rhema Harerimana said Friday, traveling with one baby nursing at her breast, another on her back and a toddler clinging to her skirt.
Harerimana said she had been on the run for five days but was heading home to Kibumba, about 17 miles from Goma.
The senior U.S. envoy for Africa, Jendayi Frazer, arrived in Goma on Friday with Alan Doss, the top U.N. envoy in Congo. French Foreign Minister Bernard Kouchner and British Foreign Secretary David Miliband were expected to visit both Goma and the Congolese capital, Kinshasa.
"The cease-fire is fragile," Doss said Friday. "It will not hold if there isn't progress on other fronts, those political and diplomatic."
The international envoys aim to get Congo President Joseph Kabila and Rwandan President Paul Kagame to sit down together and sort out the issues at the root of the conflict. EU Development Commissioner Louis Michel
- who was holding separate talks with Kabila and Kagame - said in Kinshasa that both leaders had agreed to hold a peace summit in Nairobi, Kenya.
The United Nations' deputy representative and humanitarian coordinator in Congo said more than 1 million people have been displaced
- 220,000 of them since August.