"We are victorious, we won the battle," Col. Vianney Kazarama told The Associated Press.
The M23 had split at the end of February following a dispute among the leaders of the movement. The movement's military leader, Gen. Sultani Makenga, dismissed Runiga, who was the political head of the movement. Both men then formed their own factions, which have been fighting since.
Runiga was detained by Rwandan authorities after fleeing across the border, said Kazarama, who is the spokesman for Makenga's faction. He said that Gen. Bosco Ntaganda, who has been siding with Runiga and is wanted by the International Criminal Court, is being pursued.
"Bosco has fled into the park, but we will go after him," Kazarama said.
M23 is an armed group largely made of Tutsi fighters who were part of a previous rebellion before they integrated into the army in 2009. They rebelled again in April 2012, and named themselves after the failed peace deal signed on March 23, 2009.
"The soldiers and officers from DRC that have entered Rwanda have been disarmed and detained," Rwanda's government spokeswoman Louise Mushikiwabo said Saturday. "Several wounded among them are receiving treatment with assistance from the Red Cross. We are consulting several regional and international organizations to facilitate appropriate handling of this new group of refugees."
Runiga has been detained separately for his own safety, she added in a written statement.
Col. Olivier Hamuli, spokesman for Congo's army in the North Kivu province, questioned Runiga's detention.
"Is it an arrest or are they hiding him away?" he said.
U.N. reports have alleged that Rwanda is supporting the M23 rebels, by providing them with troops, weapons and ammunitions. Rwanda denies the accusations.
The rebels took the strategic city of Goma in November 2012, but withdrew from the capital of North Kivu two weeks later after the Congolese government agreed to negotiate with them. However, the rebels kept their positions just outside Goma, within two kilometers (miles) of the city's airport which is guarded by U.N. peacekeepers.
The split within the rebellion called into question negotiations with the government, entered into after the seizure of Goma.
M23 rebels and the government have been hashing out an agreement since December, and were supposed to sign an accord by March 15. But the Friday deadline passed without a consensus because of the divide in the rebel group.
Runiga's faction had claimed it is the only one entitled to negotiate with the Congolese government since the leader of the M23 delegation for ongoing negotiations in Uganda is still loyal to Runiga. However, Kazarama said that his faction will now continue government negotiations.
"We had an internal problem, now that this has been solved, we will be able to carry on the negotiations with the government," he said Saturday.