A leader of Congo's M23 rebels has defied a deadline imposed by a regional group of nations, saying the insurgents will stay in the key eastern city of Goma.
He said the rebels will fight the Congolese army if it tries to retake it.
Underscoring the volatility of the situation, a different rebel group, the FDLR, crossed into neighbouring Rwanda and attacked Rwandan army positions, according to local Congolese villagers and M23 rebels.
There was no immediate comment from authorities in Rwanda.
Speaking in Goma, M23 president Jean-Marie Runiga said the rebels will not leave the city of one million which they seized a week ago as United Nations peacekeepers looked on.
The deadline imposed by the International Conference on the Great Lakes Region for the rebels to depart was midnight Monday.
Congolese government troops were in the town of Minova, 60km south of Goma, but they appeared disorganised and not in position to launch an immediate assault on the city which is at the center of eastern Congo's lucrative diamond and minerals mines.
The M23 was created seven months ago by former rebels who joined and then defected from the Congo army.
The group is supported by Rwanda and Uganda, according to a United Nations report released last week, and has been accused of human rights abuses, including executions and forced recruitment of children.
"The M23 only wants peace," Mr Runiga said. "But we give ourselves the right to defend ourselves and to push back the enemy as far as we deem necessary."
In a possibly-related development, fighting erupted about 30km north of Goma in Kibumba, near the Rwandan about 5am, said an M23 officer, who would only give his name as Lt Paluku, and Kibumba residents.
Hours later AP journalists saw FDLR rebels - who are enemies of the M23 - retreating back into Congo from the border.
About 100 M23 fighters were pursuing the FDLR fighters.
The FDLR is a French acronym for the Democratic Force for the Liberation of Rwanda, a group of Hutu extremists, many of whom are blamed for leading Rwanda's 1994 genocide of Tutsis.
FDLR members fled to eastern Congo after the genocide.
The M23 are mainly Tutsis who defected from the Congolese army in April this year.
Runiga said Congolese army troops were also involved in Tuesday's clashes, and that they were fighting alongside the FDLR. The claim could not be independently verified.
"We have learned that the FARDC (the Congo army) with its FDLR allies have attacked Rwanda," said Runiga.
The Rwandan army spokesman was in a meeting and not available for comment.