Russ Feingold, the United States special envoy for the Great Lakes region of Africa, said Wednesday that the two sides should “sign a final, principled agreement that provides for the disarmament and demobilization of the M23 and accountability for human rights abusers.”

Mohammed Adar, the representative for the United Nations High Commissioner for Refugees in Uganda, said about 5,000 refugees had streamed into Uganda from the Bunagana area in the past 24 hours. “We are also getting reports that some M23 elements have also come, but just very small numbers,” he said, including nine combatants who had surrendered to the Ugandan military.

Another United Nations official reported that 33 combatants from the rebel group had surrendered to peacekeepers this month. Many more surrendered to the Congolese military. Displaced people were returning to their homes in the town of Kibumba and surrounding areas, the United Nations also said, the scene of heavy fighting over the weekend as rebels dug in and the military fought to displace them.

Rich in valuable minerals, eastern Congo has been troubled by conflict for decades. The M23, which named itself after March 23, 2009, the date of a failed peace deal, is only the latest group to destabilize the region.

For more than a year and a half, the M23 controlled various towns and mines and stretches of land along eastern Congo’s border with Rwanda and Uganda, even setting up a system of tax levies and local administrators. Among their safest havens was Bunagana, a short walk across the border to stable and relatively prosperous Uganda.

The military advance represented a major turnaround from a year ago, when rebels from the M23 group seized the provincial capital of Goma. That setback galvanized support for a more robust military presence in eastern Congo for the military and for the United Nations, which created a muscular intervention brigade.