Rebel fighters have entered central Goma, the main city in the east of the Democratic Republic of Congo.
A BBC correspondent there saw exchanges of small-arms fire with the Congolese army but otherwise there was little resistance.
The M23 rebels say they have captured the city, but this has not been confirmed. UN forces are reportedly still there.
Goma has a population of about 400,000. Aid agencies say tens of thousands of people have fled their homes in the last five days.
On Monday, the government rejected a 24-hour ultimatum by M23 to withdraw its forces from Goma and enter into peace talks.
Various rebels groups have been active in eastern DR Congo since the end of a war in 2003.
The M23 was formed by a group of former rebels after a mutiny in the army in April. It largely comprises ethnic Tutsis, the same group which dominates the government in Rwanda.
The DRC government accuses Rwanda of backing the rebels.