Some 80,000 people lived in Nyanzale, North Kivu province, about 70 kilometres (45 miles) from the provincial capital of Goma.
"We are under the control of the M23 here at Nyanzale," a health sector source said. "They are advancing towards Kikuku. They have a lot of vehicles," the source added asking not to be named.
The Tutsi-led M23 group were in Nyanzale, "they are heading towards the hills," a resident told AFP by telephone.
Vehicles transporting rebel troops and munitions had been driven into the town, he added, asking not to be named.
Patrick Muhindo Mongera, chief of the administrative area that includes Nyanzale, called the security situation "precarious" with attacks since Tuesday.
"This morning we can confirm the capture of Nyanzale by M23 rebels," he said, adding the local population had fled.
A security source confirmed that several locations in the Rutshuru region had been taken after reports of 15 deaths and the displacement of thousands on Monday.
"We are fighting at this moment. The enemy has taken control of the villages of Kashalira, Kirima, Ngoroba and the city of Nyanzale," he said.
M23 rebels have seized significant territory in North Kivu since taking up arms again at the end of 2021.
Kinshasa, the United Nations and Western countries say Rwanda supports the M23 in a bid to control the vast mineral resources in the region. Rwanda denies any role.
International Committee of the Red Cross (ICRC) director general Robert Mardini on Wednesday held a press conference in Goma calling events "extremely" concerning.
He said hundreds of civilians, including women and children, were pouring into health centres with serious wounds. He estimated that 40 percent of the cases were caused by shelling and heavy weapons fire in densely-populated areas.