Rebel leader General Laurent 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 1994 Rwandan genocide.
The Congolese government has often promised to stop Hutu forces from using its territory, but has not done so.
Gen Nkunda has also objected to government plans for foreign involvement in exploiting the country's vast mineral wealth.
The Congolese government has refused to negotiate with Gen Nkunda, calling him a terrorist.
With the lull in the fighting and a desperate shortage of food and water in Goma, thousands of people who sought refuge there have been leaving the city, heading to the village of Kibati, about 12km (7.4 miles) to the north.
The BBC's Peter Greste in Goma says the road from the city is choked with human misery.
Thousands of people leave Goma
For mile after mile, it is full of families bent forward with their lives on their backs: stoves, food, clothes, bedding and children.
Aid agencies have all but stopped work because of security fears.
"The whole population in Goma, and around Goma are feeling extremely unsafe," Red Cross spokesman Marcal Izard told the BBC.
"They need food, water, shelter and, most of all, protection, [and] some sense of knowing that they will not be attacked, that they will be spared by this new round of clashes."
A spokesman for the UN's refugee agency, the UNHCR, told the BBC that the situation was "extremely critical".
A Congolese aid-worker based in Goma, Godefroid Marhenge, told the BBC's Network Africa programme that some displaced people were without water or shelter, and "in desperate need of humanitarian assistance".
Oxfam and other leading international aid agencies have withdrawn international staff from the city, where a main hospital as well as numerous businesses and homes have been looted.
Gen Nkunda said on Thursday that he was opening a "humanitarian corridor" for people to return to their homes, and so that aid could reach those trapped between his forces and UN soldiers backing up government troops in the city.
Our correspondent said that instead of an open corridor, he found people hurrying back to Goma.
"Someone has been shooting at us," one breathless woman said. "We can't go any further."
But those who did reach Kibati told the BBC that they had more chance of getting food in the forests and bushes around the village than inside Goma.
Aid group Mercy Corps has begun to distribute water to the new arrivals.
Further north, the UNHCR says that it has received reports that several camps for internally displaced people near Rutshuru, about 90km (56 miles) north of Goma, have been forcibly emptied, looted and burned.
About 50,000 people are living in camps in the area, and aid workers are in the process of trying to verify the reports, the UNHRC said.
After several days of fighting, Gen Nkunda declared the ceasefire late on Wednesday, and his Tutsi forces are positioned some 15km (nine miles) from Goma - the provincial capital of North Kivu.
However, Gen Nkunda has threatened to take the city unless UN peacekeepers guarantee the ceasefire and security in Goma.
Looting, killings and rapes were reported in the city on Thursday, much of it blamed on retreating Congolese troops.
Meanwhile, intense international diplomatic efforts are going in a bid to maintain the ceasefire and bring an end to the fighting:
• The parliament in DR Congo has called on government to negotiate with Gen Nkunda, although President Joseph Kabila has previously refused to do so
• UN Secretary General Ban Ki-moon has said he is "deeply concerned" about the situation, and has called on regional leaders to take concrete measures to broker a peace deal
• EU diplomats are meeting in Brussels to discuss whether to send troops to back up UN peacekeepers, after EU envoy Louis Michel met Mr Kabila and his Rwandan counterpart Paul Kagame
• The EU is also to discuss sending troops to the area to aid the humanitarian effort
• An African Union (AU) Peace and Security Council is to hold crisis talks at AU headquarters in Addis Ababa
• US Assistant Secretary of State for African Affairs Jendayi Frazer has held talks with Mr Kabila in DR Congo's capital, Kinshasa.
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