In a statement Sunday, Ban called on the rebels "to immediately lay down their arms in accordance with the agreements reached in Kampala, [Uganda], and comply with the immediate withdrawal of their forces from Goma," RTT News reported.
Democratic Republic of Congo President Joseph Kabila, Rwandan President Paul Kagame and Ugandan President Yoweri Kaguta Museveni had earlier issued a statement calling on M23 to "stop [its] offensive and pull out of Goma."
The three presidents were among African leaders who met in the Ugandan capital Saturday and urged the rebel group to stop its fighting and threats to depose the Kabila government.
Ban urged the African leaders and M23 to "address the fundamental causes of conflict."
M23 encountered little resistance when it entered Goma Tuesday and have demanded immediate talks with Kabila. The rebels have said they intend to stay in Goma while they await talks.
Although most Congolese troops fled Goma ahead of M23's arrival, the U.N. said its 19,000-member peacekeeping force, MONUSCO, is continuing to maintain its position in the city "to protect civilians from imminent threat."
The U.N. said it had received reports M23 forces had kidnapped women and children from Goma, destroyed property and hurt civilians.