The UN says at least 2,900 people were killed during the fighting, with 2,000 bodies buried and another 900 still in the city’s morgues.
Earlier this week, the rebels announced a ceasefire on humanitarian grounds.
However, the M23 launched a new offensive on Wednesday, sources say, reportedly capturing the mining town of Nyabibwe.
Nyabibwe is about 100 km (60 miles) from Bukavu – the east’s second-largest city, and the reported target of the rebels’ most recent advance.
The Congolese authorities have enlisted hundreds of civilian volunteers to help defend Bukavu.
Meanwhile, Malawi has announced it will start preparations for a withdrawal of its peacekeeping forces from the country. This follows the killing of three of its soldiers in the fighting around Goma.
They were part of a southern African force, led by South Africa. Although 14 South Africans have been killed, President Cyril Ramaphosa has vowed to keep his forces in the country.
Back in Goma,where residents are adapting to life under the M23, there are fears of a cholera outbreak.
Stephan Goetghbuer, a regional lead from the charity Médecins Sans Frontières (MSF), said: “Access to water has been cut for days, corpses have been lying in the streets and waterborne diseases such as cholera are a real threat.
“Some of our cholera treatment centres are full and have been expanded.” BBC