Nkunda, a renegade general leading the National Congress for the Defence of the People (CNDP), had demanded direct talks with Kinshasa after government troops fled as his fighters advanced on the town of Goma.
Goma was placed under an overnight curfew on Tuesday with the CNDP maintaining the unilateral ceasefire it called last week.
The government refused to give in to the demands for talks with Nkunda saying that dialogue must be between all the armed groups operating in the region.
"There are no small and large armed groups," Lambert Mende, government spokesman, said. "The act of creating a humanitarian disaster does not give special rights."
Nkunda says his fighting to protect the rights of ethnic Tutsis in eastern DR Congo.
The DR Congo prime minister was expected to visit Goma on Tuesday as part of a tour of the region aimed at "comforting the population", a government official told the AFP news agency on condition of anonymity.
Adolphe Muzito, who took office on October 10, was also expected to visit Bukavu in South Kivu, Kisangani and Dugu.
About 850 UN peacekeepers stand between the CNDP and Goma after government troops fled in the face of the rebel offensive.
Alexis Tambwe Muamba, DR Congo's foreign minister, called on the UN Security Council to "redefine" the peacekeepers' mission to allow it to "lead more muscular operations" againt the rebels.
Bernard Kouchner, the French foreign minister who toured Congo at the weekend and met regional leaders, also said the 17,000-strong force needed tougher rules of engagement and additional troops.
|About 250,000 people have been displaced by the fighting in the past two months [AFP]
"There are entire brigades that are unable to engage in defensive, let alone offensive, action, because their rules of engagement are insufficient or they are very restrictive," he said.
An aid convoy is expected to take food supplies to some of the hundreds of thousands of people in rebel-held territory north of Goma.
"Around 250,000 people are now believed to have been displaced in the last two months, bringing the total number of internally displaced to around one million, 20 per cent of the entire North Kivu population," the UN children's agency said in a statement.
Tuesday's relief effort comes after a convoy arrived at Kibati camp, where at least 50,000 displaced people were thought to be hiding in the bush, the previous day.
The 12-vehicle convoy provided just soap and plastic jerry cans for holding water in an attempt to guard against a potential cholera outbreak, sparking anger among the refugees who were hoping for food.
"Everybody is hungry, everybody," said Jean Bizy, a 25-year-old teacher who added that he had been surviving on wild bananas for days.
UN officials admitted there were serious problems with hunger at Kibati camp, but said their priority was resupplying clinics looted by retreating government troops.UN envoy
In New York, Ban Ki-moon, the UN secretary general, appointed Olusegun Obasanjo, the former president of Nigeria, as his special envoy to defuse the crisis.
Ban also said he was prepared to travel to the region as early as this weekend for talks with Joseph Kabila, the DR Congo president, and Paul Kagame, his Rwandan counterpart.
"There can be no military solution to the crisis in eastern Congo. Our efforts must focus on political negotiation," he said.
"To that end I have held repeated conversations with Presidents Kabila and Kigame, directly and through my envoys. I'm also working closely with world leaders."