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.

Rwandan-backed M23 rebels asserted their control over east Congo's largest city Goma on Thursday by calling on residents to resume normal life, even as the group clashed with Congolese troops as they tried to take more territory.

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.