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.

The United States, France and Britain pressured Rwanda on Sunday over its support for rebels rapidly closing in on eastern Congo's largest city, as government forces struggled to halt an offensive that has forced thousands of civilians to flee.

Rwandan President Paul Kagame blasted criticism of his country's role in eastern Democratic Republic of Congo where rebels his government backs have seized its largest city, saying Kigali is prepared for "confrontation" if necessary.