This comes as the United Nations says thousands of civilians have fled a battle zone in the region, sparking fears of a renewed civil war.
“The army is in a state of alert and its units are currently deploying… to the eastern provinces,” said DRC President Joseph Kabila during a televised address, in the first official reaction to the infiltration reports.
“We will never bow to this new threat to the transitional institutions in our country,” he said.
“Rwanda has goals that are political, economic, exploitative and predatory.”
Members of the UN Security council are meeting in New York to discuss the reports.
Bernard Le Flaive of the UN’s Office for the Coordination of Humanitarian Affair said “several thousand” civilians are fleeing to Kanya, Kanyabayunga and Kirumba, settlements around 150 kilometres north of Goma, on the Rwandan border.
A statement released by Rwandan rebel group the FDLR said “several battalions” of the Rwandan army has arrived in the DRC.
Mr Le Flaive did not identify whom the rebels are fighting, but said civilians came from areas north of Rutshuru and Walikale.
“They are fleeing fighting operations against the FDLR,” he said.
“Atrocities are also taking place. We expect more displaced in the coming days,” he added.
The FDLR is the organisation adopted by the Hutu extremists who fled Rwanda after carrying out much of the killing during the 1994 genocide.
A civil war in the late 1990s claimed up to three million lives.
The UN said it has aerial photographs and ground sightings that strongly indicate that Rwandan troops have crossed the border.
Evidence includes encounters with soldiers appearing to carry Rwandan military gear, and the sighting of a 100-soldier contingent of soldiers of Rwandan appearance.
Rwanda has invaded the mineral and resource-rich Congo twice since 1996, apparently in search of Rwandan Hutu rebels.
The 1998 invasion sparked a war that drew in the armies of a half dozen African nation, leaving more than three million people dead.