Rwanda-backed fighters advanced on a second front in their offensive across eastern DR Congo on Wednesday after seizing control of most of the key city of Goma during heavy fighting with the Congolese military.

The weeks-long advance by the M23 armed group prompted calls from mediator Angola for urgent talks, as well rising international criticism and warnings of a looming humanitarian crisis.

DR Congo has called on the world to stop the M23's march across the vast central African country's mineral-rich east, wracked by decades of conflict that can be partly traced back to the 1994 Rwandan genocide.

After days of intense clashes, calm returned to Goma, provincial capital of North Kivu, on Wednesday as residents started venturing from their homes.

Despite international pressure to end the crisis, Congolese President Felix Tshisekedi declined to attend talks with his Rwandan counterpart Paul Kagame on Wednesday.

At a videoconference summit of the East African Community, the regional bloc's heads state "called for peaceful settlement of the conflicts", it said in a statement.

M23 fighters and Rwandan troops entered Goma on Sunday, progressively seizing the city's airport and other sites of the key mineral trading hub.

The latest fighting has heightened an already dire humanitarian crisis in the region, causing food and water shortages and forcing half a million people from their homes this month, according to the United Nations.

On the other side of the country, furious protesters in the capital Kinshasa on Tuesday attacked the embassies of various nations they accused of not stepping in to halt the chaos in the east.

After protesters burnt tyres in the streets and looted supermarkets, the authorities banned all further protests in the capital, which remained calm on Wednesday.

The United States, which was among the nations whose embassy was targeted, ordered non-emergency staff and their families to leave the country.

DR Congo's former colonial ruler Belgium also warned its citizens against travelling to the country, while Brussels Airlines scrapped flights to Kinshasa. (AFP)