Congo's military accused Rwanda of "no less than an invasion" after M23 rebels captured a key town.
The military vowed that Congolese forces would defend their homeland, marking a dramatic escalation in tensions between the two Central African neighbours.
The statement from General Sylvain Ekenge, spokesman for the military governor of North Kivu province, came hours after the town of Bunagana fell into the hands of the M23.
"The Rwandan defence forces have this time decided to violate ... our territorial integrity by occupying the border town of Bunagana," the military said in a statement, adding that it constituted "no less than invasion of the Democratic Republic of Congo."
There was no immediate reaction from the government of Rwanda, but the government there has strongly denied accusations over the years that is supports the Congolese rebel group.
Many of the M23 fighters are Congolese ethnic Tutsis and Rwanda's president is of Rwandan Tutsi descent.
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.
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 kilometres northeast of Goma, which also serves as a hub for international aid organisations and the UN peacekeeping mission known as MONUSCO.
Bunagana is also an important transit point for goods being imported into Congo from as far away as China.
A day earlier, a government official had accused the rebels of wanting to seize Bunagana in order to financially paralyse Goma.