Members of the March 23 Movement in DRC rebelled against the government early this year. Its leader, Bosco Ntaganda, is suspected of conscripting child soldiers into the rebel group.
Ban sent a message to a regional conference in Uganda warning of the continued threat posed by M23.
"The M23, (which) has recently made advances northward from its positions in (DRC's eastern province of) North Kivu, is continuing destabilizing activities in areas that it occupies, and is perpetrating serious human rights violations, including child recruitment and sexual violence," his message stated.
More than 260,000 people in North Kivu province have been displaced by rebel fighting, the United Nations estimates.
Ban warned that support for M23 and other rebels in DRC should "cease immediately and permanently."
Rwanda was suspected of supporting the rebel movement, an allegation the government denies.
U.N. and regional authorities are examining a proposed deployment of an international neutral force to regions along the DRC-Rwanda border.