Gunfire rippled across east Congo's largest city Goma where Rwandan-backed M23 rebels still faced pockets of resistance from army and pro-government militias on Tuesday, while another four South African peacekeepers were killed.

The rebels marched into the lakeside city of two million people on Monday in the worst escalation since 2012 of a three-decade conflict rooted in the Rwandan genocide and control of natural resources.

Dozens of Democratic Republic of Congo troops had surrendered, but some soldiers and pro-government militiamen were holding out, residents and UN sources said.

People in several neighbourhoods reported small arms fire and some loud explosions on Tuesday morning.

"I have heard the crackle of gunfire from midnight until now ... it is coming from near the airport," an elderly woman in Goma's northern Majengo neighbourhood, close to the airport, told Reuters by phone.

The UN and global powers fear the conflict could spiral into a regional war akin to those of 1996 to 1997 and 1998 to 2003 that killed millions, mostly from hunger and disease.

Corneille Nangaa, leader of the Congo River Alliance that includes the M23, has suggested the rebels' aim is to replace President Felix Tshisekedi and his government in the capital Kinshasa, more than 1,500 km west of Goma.

In the latest diplomatic efforts, South Africa said its President Cyril Ramaphosa and his Rwandan counterpart Paul Kagame agreed in a phone call on the need for a ceasefire.

But on the ground four more South African peacekeepers in Congo were killed, South Africa's military said, bringing the number of its fatalities in the past week to 13.

Of the latest deaths, three were caught in crossfire between the Congolese army and the M23 on Monday, while another succumbed to wounds from fighting with the rebels, it said.

'POWDERKEG TOWN'
Willy Ngumbi, a bishop in Goma, said bombs had hit a house where priests were staying and the maternity ward of a Catholic hospital on Monday.

"The town is a powderkeg," he said by phone. "The youth are armed and the fighting is now taking place in the town."

The International Committee of the Red Cross said on Monday it had treated 117 injured people, including 86 with bullet wounds, at a hospital in Goma that it supports.

Also on Monday, Congolese soldiers and Rwandan troops exchanged artillery fire near the border, with Rwanda's army reporting five people killed and 26 injured.

The fighting has sent thousands of people streaming out of Goma, which has been a vital regional hub for humanitarian aid for displaced people. Hundreds of thousands have fled fighting since the start of the year - on top of 3 million who were displaced in eastern Congo last year.

Goma is also a gateway for trade of tantalum and tin ores, used in phones and computers.

"The city is in real difficulty and if it hasn’t fallen overnight, it will in the coming days," French Foreign Minister Jean-Noel Barrot told Sud Radio. "Rwanda must put down its weapons, calm must return and dialogue needs to restart."

FAST OFFENSIVE
M23 is the latest in a string of ethnic Tutsi-led, Rwandan-backed insurgencies. Its fighters took up arms again in 2022, a decade after a previous insurgency that briefly captured Goma.

In recent weeks they made swift gains through North Kivu province, on the border with Rwanda, ignoring calls from world leaders to halt their offensive.

Rwanda has dismissed calls for troops to leave, saying its security is threatened and blaming Kinshasa for sabotaging peace efforts. UN experts say Kigali has deployed 3 000. to 4 000 troops in eastern Congo to support the M23.

Congo's government has called on international powers to pressure Rwanda, potentially via sanctions, to end the M23 offensive.

US Secretary of State Marco Rubio spoke with Congo president Tshisekedi on Monday, the State Department said. "Secretary Rubio condemned the assault on Goma by the Rwanda-backed M23 and affirmed the United States’ respect for the sovereignty of the DRC," it said.

The UN Security Council was due to discuss the crisis again on Tuesday, diplomats said.

In Kinshasa on Tuesday, dozens of young men burned tyres and chanted anti-Rwanda slogans.

Rwanda says ethnic Hutu militias, some with links to the extremists who murdered close to one-million Tutsis and moderate Hutus during the 1994 genocide, threaten its security.