In this latest fighting the Tutsi rebels clashed with Pareco Mai-Mai forces mainly made up of Congolese Hutus, who Gen Nkunda alleges are backed by the government.
Witnesses reported killing and looting, and some people were wounded, a BBC correspondent who travelled to the town said.
Tens of thousands of displaced people are already in and around Goma, which Gen Nkunda has threatened to attack - though the ceasefire around the city appears to be holding for now.
In a significant hardening of their position, UN peacekeeping troops in Goma - who are reinforcing their position - have been ordered to fire on any armed groups trying to enter the city.
The fighting at Kiwanja, near the Rutshuru, has forced some aid workers to suspend their activities a day after bringing in the first food convoy to rebel-held territory.
The UN refugee agency says three camps for displaced people near Rutshuru have been emptied and destroyed.
The agency has been trying to establish the fate of about 50,000 people who had been sheltering in the area.
The BBC correspondent who was in Kiwanja said a UN convoy that travelled north from Goma had so far only been able to deliver food and beer to the peacekeepers.
The convoy had turned back to Goma after the most recent outbreak of fighting, he said.
Gen Nkunda has threatened to topple the DR Congo government in Kinshasa, 1,580km (980 miles) west of Goma, unless President Kabila agrees to hold direct talks.
The militia attacked Nkunda's rebels in territory they took last week
He has said his forces are now free to pursue their offensive, accusing the government of breaking the ceasefire.
Correspondents say the militia involvement in the fighting makes any push for negotiations between Gen Nkunda and the government more complicated.
The latest clashes sparked fears the rebels could follow through on their threat to attack Goma - or target Masisi, a hub for Rwandan Hutu rebels west of Goma where aid workers have been evacuated and that is now surrounded by Gen Nkunda's men.
The BBC's Peter Greste in Goma says the rebel threat against Kinshasa could be hubris, as it is hard to see how he could transport between 6,000 and 7,000 fighters all the way across a country the size of western Europe.
The rebel forces do, however, appear to have the strength to take Goma, he said.
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