About 200,000 people fled their homes after fighting resumed in the area in late August.
The United Nations says many refugees are malnourished and some are dying of hunger.
Ron Redmond of the UN refugee agency says it almost impossible to reach those in need of help.
"We simply cannot send teams out into the countryside. There's too much fighting going on; it's too dangerous; it's anarchy," he said.
"There are already some 800,000 to a million people internally displaced in this region, so it's really a huge population in need of help."
Rwanda has been accused of backing Gen Nkunda, who left the army and launched his own low-level rebellion after DR Congo's civil war ended.
He says he is fighting to protect the minority Tutsi community from the Hutu militia which carried out the 1994 genocide in Rwanda.
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 - whose main strongholds are in Kichanga in the Masisi Mountains and Bunagana town bordering Uganda - has always refused to disarm while Rwandan Hutu rebels still operate in the area.
Many Congolese say that Rwanda is helping Gen Nkunda's forces, something that both Rwanda and the UN have denied.