On Monday, in the latest escalation, M23 fighters captured the strategic town of Bunagana on the Ugandan border.
A report by the UN's international team of experts on the DRC, dated June 14 but published on Friday, suggested that the move is part of a plan to strangle access to Goma and eventually capture the city.
It said the resurgence of M23 violence stemmed in part from stalled negotiations with the Congolese government.
According to interviews with six M23 fighters, the group's leader General Sultani Makenga planned to capture Bunagana and two other towns in eastern North Kivu province "to cut off the strategic Goma-Rutshuru road, and then take Goma," the report said.
The intention is to extract political concessions that include amnesties, asset recovery, political positions and integration of M23 fighters into the Congolese army, according to the report.
Goma is an important commercial hub of about a million people in DRC's east, which lies on the Rwandan border.
Recent fighting between the rebels and Congolese troops has inflamed regional tensions, with the Democratic Republic of Congo's government accusing neighbouring Rwanda of backing the M23.
Rwanda has repeatedly denied the charge. Both sides have accused each other of cross-border shelling.
A primarily Congolese Tutsi militia that is one of scores of armed groups in eastern DRC, the M23 leapt to global prominence in 2012 when it briefly captured the city.
It was forced out shortly afterwards in a joint offensive by UN troops and the Congolese army.
After lying dormant for years, the rebels resumed fighting last November after accusing the government of failing to honor a 2009 agreement under which the army was to incorporate its fighters.
Clashes intensified in March, causing thousands of people to flee.
Meanwhile, the friction between Kinshasa and Kigali has escalated to the point where a break in relations may be forthcoming.