“In the event of a new threat against our positions or the civilian population, our movement's troops have received the order to follow and annihilate the threat no matter where it comes from,” M23 spokesman Willy Ngoma said in the statement.
Relations between Rwanda and Congo have been fraught for decades. Rwanda alleges that Congo gave refuge to the ethnic Hutus who carried out the 1994 Rwandan genocide that killed at least 800,000 ethnic Tutsis and moderate Hutus. The two countries have long accused each other of supporting various rival armed groups.
Late last month, Rwanda’s military accused neighboring Congolese forces of injuring several civilians in cross-border shelling.
The M23 rose to prominence more than a decade ago when its fighters seized Goma, the largest city in Congo's east which sits along the border with Rwanda. After a peace deal, many of M23's fighters were integrated into the national military.
Then earlier this year the group appeared to make a comeback, launching an offensive against Congo's military after saying the government had failed to live up to its decade-long promises.
The key town that was seized Monday, Bunagana, is only 60 kilometers (37 miles) northeast of Goma, which also serves as a hub for international aid organizations and the U.N. peacekeeping mission known as MONUSCO.
Bunagana, near the border with Uganda, is also an important transit point for goods being imported into Congo from as far away as China.
In Uganda, police spokesman Fred Enanga said Monday that more than 100 Congolese soldiers, fleeing fierce fighting with rebels, crossed the border and “surrendered” to Ugandan officials. He said the Congolese soldiers will be moved to Rutshuru, another eastern Congo town near the Uganda border.
While the rebels claimed they took the town of Bunagana in order to stabilize it, local leaders on Monday urged Congo's military to reclaim it.
“We deplore the M23 rebel attack and call on the Congolese government to track down and neutralize these rebel groups so that state authority can return,” said Innocent Ndagije, a civic leader in Bunagana.
Associated Press writers Rodney Muhumuza in Kampala, Uganda and Krista Larson in Dakar, Senegal contributed.