Government forces reportedly retreated as the rebels advanced.
The rebels, loyal to renegade Gen Bosco Ntaganda, who is wanted for war crimes by the International Criminal Court, took up arms in April.
"We appeal to the international community to do something to protect the civilians who fled the fighting and are living in fear," Omar Kavota, a local official in Rutshuru, said to the Associated Press.
Rutshuru lies 70km (43 miles) to the north of the provincial capital Goma.
An Indian peacekeeper was killed as the rebels took control of the Democratic Republic of Congo side of the town of Bunagana on Friday, the UN said.
The rebels defected from the army after pressure increased on the government to arrest Gen Ntaganda, when one of his former colleagues was convicted of recruiting child soldiers by the ICC.
Some 200,000 people have fled their homes since April, with about 20,000 crossing the border to Uganda and Rwanda.
A recent UN report has accused Rwanda of backing the rebels - Gen Ntaganda is an ethnic Tutsi, like the majority of Rwanda's leadership.
But Rwanda has vehemently denied the accusations.