The group, which has the backing of Rwanda, has recently captured the key cities of Goma and Bukavu in the east of the country.
Dozens of people are reported to have been hurt by two explosions that went off during a meeting between M23 rebel leaders and residents in eastern Democratic Republic of Congo (DRC).
The attack took place in the city of Bukavu, which M23, a Rwanda-backed group, seized earlier this month.
Videos and photos posted on social media show a crowd of people fleeing the scene, with bloodied bodies lying on the ground.
A journalist who was present at the meeting said that the blasts rocked the area as rebel leaders were leaving the podium. They included Corneille Nangaa, who runs the Congo River Alliance (AFC), of which M23 is a member.
Eastern DRC, an area rich in valuable minerals, has suffered decades of fighting.
Over the last few months, M23, one of many armed groups vying for control in the region, has achieved a series of sweeping victories against the national army.
In January, the rebel group captured Goma, the largest city in the east of the country, before taking Bukavu, the second largest, soon afterwards.
They have even vowed to seize the capital, Kinshasa, which is over 1,600km away.
More than 7,000 people have been killed during this year’s surge in fighting, according to DRC Prime Minister Judith Suminwa Tuluka, who said the security and humanitarian situation in the east had reached “alarming levels”.
UN experts say that M23, whose soldiers have been accused of rape and of killing children, is supported by roughly 4,000 Rwandan troops.
As M23 attempts to capture more territory, pressure is growing on Rwanda from international actors such as the European Union.
Kaja Kallas, the EU’s top diplomat, has called DRC’s territorial integrity “non-negotiable”, saying the bloc will review its raw materials deal with Rwanda in light of its support for M23.
While M23 claims it is seeking to protect ethnic Tutsis and people of Rwandan origin in the region, analysts say Rwanda is using this as a pretext for its involvement.