The March 23 Movement is said to have occupied Goma, the capital of North Kivu province in eastern Democratic Republic of Congo.
British Foreign Secretary William Hague called on M23 forces to pull out of the city "immediately" and allow "legitimate" forces to restore control to the city.
"I condemn in the strongest possible terms the entry into Goma by M23 militia on Nov. 20," he said in a statement. "I urge once more those with influence over the M23 to encourage them to stop fighting and to withdraw immediately."
The governments of neighboring Rwanda and Uganda are accused of supporting the rebel movement, an allegation they each deny.
Hague said he sent Mark Simmonds, British minister for Africa, to the region to discuss the situation personally with his counterparts.
Non-governmental agencies in the area said conflicts in eastern DRC has displaced tens of thousands of people. The BBC reports that DRC President Joseph Kabila called on Congolese citizens to resist the rebellion.
A senior rebel commander told the BBC that if Kabila's government isn't interested in negotiating, the rebel movement would occupy more positions in eastern DRC.
"I call on all sides to work together to find a sustainable long-term solution to the current crisis without recourse to further violence," said Hague.