The M23 rebels east of the Democratic Republic of Congo entered Bukavu, the second largest city in the eastern region.
Corneille Nangaa, head of the Congo River Alliance, which includes the rebels of M23, told the news agency in Reuters that the rebels had entered the provincial capital in southern Kivu on Friday evening and would continue their lead on Saturday.
The progress of militants supported by Rwandans arise despite international calls to a ceasefire and a resumption of peace talks.
Hundreds of thousands of people have been forced from their homes in recent weeks following the rebellious advance.
Last month, the M23 led by Tuts, which was supported by neighboring Rwanda, seized Goma, the main city of the East rich in minerals. The Congolese government accuses Rwanda of sowing chaos in the region in order to benefit from its resources, an assertion of Rwanda has denied.
The M23 briefly captured Goma in a previous conflict in 2012, but the taking of Bukavu, which is the capital of the Southern Kivu province, would represent a new phase in recent turbulent history of the region.
The city, which borders Rwanda, is at the southern tip of Lake Kivu and is an important transit point for local mineral trade.
Earlier Friday, rebel fighters had entered the airport about 30 km (19 miles) north of Bukavu, while the Congolese army and a militia combined with it withdrew without having a lot of resistance.
But there were heavy clashes on the outskirts of Bukavu, the vice-government in southern Kivu, Jean Elekano, told the BBC.
In a village further north – Mayba – 70 bodies were found in a church, according to local media.
A coordinator of the local community in North Kivu, Vianney Vitswamba, told the news agency Dr Congo 7sur7 that the bodies had been found linked. The rebels of the Allied Democratic Forces (ADF) – a group linked to the Islamic State – have been blamed, but the BBC did not confirm the report.
Bukavu residents contacted by the BBC said that the authorities advised residents to stay inside.
Speaking at the Munich Security Conference, Dr. Congo, Félix Tshisekedi, called on Rwanda to be sanctioned, accusing him of “expansionist ambitions”, reports the news agency AFP.
“We will no longer bear our strategic resources during looting for the benefit of foreign interests under the accomplice gaze of those who feed on chaos,” he said.
In addition to being accused of having supported the rebels, which Rwanda denied, the country would also have its own troops in the eastern Dr. Congo.
Rwandan President Paul Kagame said his country’s priority was security. He said Rwanda was in danger of Hutu Rebels in Dr. Congo and rejected any threat of sanctions.
The news of the latest advance comes when the heads of state of the continent should meet during a summit of the African Union (AU) in Ethiopia on Saturday.
The head of the AU committee, Moussa Faki Mahamat is cited by AFP saying that a cease-fire “must be observed” adding that “military campaigns will not solve these problems. There is mobilization General of Africa today on this question and I hope that we can impose this ceasefire “.
Additional report by Alfred Laseck.
