Rwanda-backed rebels who have captured eastern Congo’s largest city say they plan to take their rebellion to the capital and seek to gain political power.

After three years on the run from the Rwandan-backed M23 insurgency in eastern Congo, on Sunday, with the rebels fighting their way into Goma's city outskirts, Colleta Nzambonimpa found herself in church with nowhere left to turn.

President Paul Kagame said Rwanda was ready for "confrontation" as he rejected criticism over his backing for M23 rebels who were pushing south on Thursday in eastern Democratic Republic of Congo after capturing the major city of Goma.