The UN Security Council has urged the rebel leader to implement the ceasefire.
An emergency session of the council also expressed alarm over cross-border firing between DR Congo and Rwanda.
The 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.
Oxfam said national staff had been advised to stay at home, but it was hoping to resume humanitarian work for more than 65,000 people in Goma's camps soon.
Another aid group, Merlin, said it had been unable to reach an estimated 150,000 people who had fled the chaos on Wednesday.
Medical charity Medecins Sans Frontieres (MSF) said it was reinforcing its staff in Congo.
Gen Nkunda has written a letter to the UN mission in Goma saying he would open a "humanitarian corridor" for aid to reach the thousands of people who are trapped between his rebel forces and the positions of the UN and Congolese government troops.
Many of the latter have fled the combat zone and some have been blamed for looting in Goma.
Overnight, Goma resident Tawite Anthony told the BBC that there were "uncontrolled soldiers who were looting all over the city".
He said he had seen the dead body of one man who had apparently been shot by the police while trying to break into a shop.
Some people were fleeing to Rwanda, he said. "Everybody's afraid of the wars. They are fearing what will happen next."
The BBC's Thomas Fessy in Goma said the atmosphere was calm but tense after a night of gunfire and looting.
He said he had seen a body with bullet wounds, but was still unclear how many people had been killed or injured.
UN peacekeepers and residents in the city of Goma
Earlier, UN Secretary General Ban Ki-moon called for an immediate end to the fighting, which he said was creating a "humanitarian catastrophe".
Mr Ban said he deplored the deliberate targeting of civilians and their use as human shields and said UN peacekeepers were "doing everything possible to protect civilians and fulfil their mandate in untenable circumstances".
Correspondents say the 17,000-strong UN force in DR Congo - the world's largest - is stretched to breaking point.
Gen Nkunda 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.
A peace deal was signed in Goma between the government and various rebel groups at the end of January.
Although he signed the deal, Gen Nkunda has refused to disarm while Rwandan Hutu rebels still operate in the area.
The AP news agency reported Mr Nkunda as saying on Thursday that he wanted direct negotiations with the government about security and his objections to a $5bn (£3.1bn) deal that gives China access to the region's mineral resources.
Some observers say that the fighting in eastern DR Congo is really over control of such resources.
Rwanda has denied claims that it is backing Gen Nkunda.
US assistant Secretary of State for African Affairs Jendayi Frazer has said she had no evidence that Rwanda was directly involved in the fighting.
Rwandan Foreign Minister Rosemary Museminali was due to meet Congo's President Joseph Kabila in Kinshasa on Thursday, AFP news agency reported.
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