The Congo River Alliance, a coalition of rebel groups that includes the M23, said in a statement that its fighters "decided to assist the population of Bukavu" in addressing its security challenges under the "old regime" in the city of 1.3 million people.
"Our forces have been working to restore the security for the people and their property, much to the satisfaction of the entire population," alliance spokesman Lawrence Kanyuka said on Sunday.
The rebels saw little resistance from government forces against the unprecedented expansion of their reach after years of fighting.
Congo's government vowed to restore order in Bukavu but there was no sign of soldiers.
Many were seen fleeing on Saturday alongside thousands of civilians.
The M23 are the most prominent of more than 100 armed groups vying for control of eastern Congo's trillions of dollars in mineral wealth that is critical for much of the world's technology.
The rebels are supported by about 4000 troops from neighbouring Rwanda, according to United Nations experts.
The fighting has displaced more than six million people, creating the world's largest humanitarian crisis.
Bernard Maheshe Byamungu, one of the M23 leaders who has been sanctioned by the UN Security Council for rights abuses, stood in front of the South Kivu governor's office in Bukavu and told residents they had been living in a "jungle".
"We are going to clean up the disorder left over from the old regime," Byamungu said, as some in the small crowd of young men cheered the rebels on to "go all the way to Kinshasa", Congo's capital.
Congo's communications ministry acknowledged that Bukavu had been "occupied" and said the government was "doing everything possible to restore order and territorial integrity" in the region.
Unlike in 2012, when the M23 briefly seized Goma and withdrew after international pressure, analysts have said the rebels this time are eyeing political power.
The fighting in Congo has connections with a decades-long ethnic conflict.
The M23 says it is defending ethnic Tutsis in Congo.
Rwanda has claimed the Tutsis are being persecuted by Hutus and former militias responsible for the 1994 genocide of 800,000 Tutsis and others in Rwanda.
Many Hutus fled to Congo after the genocide and founded the Democratic Forces for the Liberation of Rwanda militia group.
Rwanda claims the militia group is "fully integrated" into the Congolese military.
Congolese President Felix Tshisekedi, whose government on Saturday asserted that Bukavu remained under its control, has warned of the risk of a regional expansion of the conflict.
The conflict was high on the African Union summit's agenda in Ethiopia at the weekend, with UN Secretary-General Antonio Guterres warning it risked spiralling into a regional conflagration.
