In a letter to the UN mission in Kinshasa, the rebels said that they were opening humanitarian corridors for refugees camped outside the city.
However, residents fear that the CNDP will overrun the city if negotiations with Nkunda are not met.
'Allied to terrorists'
Nkunda, speaking exclusively to Al Jazeera, accused the Congolese government forces of being "allied to terrorists".
"Seeing the government using negative forces toward its people, it's a national problem.
Laurent Nkunda, speaking to Al Jazeera
"We have the most disciplined army in all of Congo and it is known by all of the international community," Nkunda said. "We are not involved in looting or raping.
"We asked for, many times, a ceasefire and peace talks, but they [the government] weren't accepting this. Many times we've been attacked by government forces."
"We are asking for freedom and we also have to fight for it ... We have to suffer sometimes to be free forever," he said.
When asked what he would do if the government didn't respond in the way that he desired, Nkunda said: "We will push the threat so far from Goma, so far from Congo. If they [the government] are not ready to talk, we are ready to push them so far from Goma, so far from Congo."
'Weak central government'
Marie-Roger Biloa, editor of Africa International, a monthly news magazine, told Al Jazeera that the central government in the DRC is very weak.
"There really is not much that the government can do in this conflict," she said.
"Despite the international community expressing its support, the rebels clearly have the upper hand here, and it is ultimately dialogue that is needed, not further violence."
The Kinshasa government accuses neighbouring Rwanda of supporting Nkunda, an ethnic Tutsi.
"The government of Rwanda is not in this conflict," Louise Muchikiwabo, Rwanda's minister of information, told Al Jazeera, saying it was a conflict between two Congolese parties.
According to the International Committee of the Red Cross (ICRC), the humanitarian situation in Goma is "catastrophic," with two hospitals have been sacked by looters on Thursday.
Government forces were reported to have fled on Wednesday night, relocating their tanks to the south on the road to Bukavu, in Sud-Kivu province.
However, accusations have been made of government forces, who have abandoned their posts, carrying out violence, including steeling and raping.
UN tanks had been drawn into position around the peacekeeping force's headquarters near the airport to the north of Goma. Madnodje Mounoubai, a UN spokesman, said that peacekeepers were also deployed at other strategic points.
Alain Le Roy, the head of UN peacekeeping operations, said an estimated 800 troops from the UN mission in DRC (Monuc) were currently patrolling Goma.
"We are trying to bring additional troops to protect the civilians in Goma in the coming three to seven days," he said. The reinforcements would be sent from other parts of DR Congo where Monuc has about 17,000 troops.
Julien Mpaluku, the governor of Goma, said that the UN remained in control of the city but "people are stampeding and panicking.
People carrying whatever they could carry streamed out of Goma on Wednesday, while another 45,000 refugees fled a makeshift camp in the nearby village of Kibati.
The camp, just north of Goma, had seen an influx of 30,000 people over the past three days joining the 15,000 already there, after the CNDP launched a major offensive in the North Kivu region.
Ban Ki-moon, the UN secretary-general, has warned that the conflict "is creating a humanitarian crisis of catastrophic dimensions, and threatens dire consequences on a regional scale".
US officials were among those who pulled out of the city and Jendayi Frazer, the US assistant secretary of state for African affairs, was expected to arrive in DR Congo's capital on Thursday.
Before departing for Kinshasa, Frazer urged Nkunda's forces to comply with previous agreements aimed at ending the conflict in the east of the country.
"I should say, they should not go into Goma, they will be held accountable for actions taking place," Frazer said in Nairobi.
Jean-Maurice Ripert, France's ambassador to the United Nations, said that he hoped that "Nkunda will announce that he stops his offensive" after declaring the ceasefire.
He also said he was planning to send a high-level envoy soon to support an initiative by Ban to facilitate dialogue between Rwanda and Congo.
Ban has reportedly been "alarmed" by reports that Rwandan soldiers were involved in the fighting against Congolese government forces, while the UN Security Council expressed concern at "reports of heavy weapons fire across the Democratic Republic of Congo-Rwanda border".