But Nkunda said his National Congress for the Defence of the People (CNDP) had some conditions for the government.
"We want them also to cease firing, because they are the ones attacking us. Second, we want them to respect humanitarian laws, because they are killing [people].
"And we want them to accept that we can have a mediator, so that we can really have peace talks."
In a letter to the UN mission in Kinshasa, DRC's capital, the rebels said that they were opening humanitarian corridors for refugees camped outside the city.
Tens of thousands of residents, refugees and government troops have fled Goma, despite rebel forces declaring a ceasefire.
Sporadic gunfire could still be heard on Thursday night in Goma, the provincial capital of eastern Congo, but the city was calm for much of the day.
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 having 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, fleeing government forces have been accused of carrying out violence, including theft and rape.
|The UN said Congo was facing a "humanitarian crisis of catastrophic dimensions" [AFP]
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.
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 was "creating a humanitarian crisis of catastrophic dimensions, and threatens dire consequences on a regional scale".