Army chief wounded
The clashes are the heaviest fighting in months in the region, following the collapse of a peace deal in October.
General Abdelkarim Bahar Mahamat Itno, the head of the Chadian army, told Al Jazeera he had been wounded in the fighting:
"We, as leaders in the army, must take part in the battles. Since we are fighting, injury is a possibility. Here I am, suffering an injury, but minor."
The FPRN, led by Adoum Yacoub, an ex-colonel, is a minor rebel group compared to Chad's main rebel factions, analysts say.
The Rally of Forces for Change (RFC) and the Union of Forces for Democracy and Development (UFDD), the two main anti-government forces in Chad, have said recently they are co-ordinating their battle against Idriss Deby, the president.
The Chadian army clashed with RFC forces on Tuesday in the east of the country near the border with Sudan's Darfur region, prompting warnings from the UN of an impending refugee crisis.
Herve Morin, the French defence minister, has said European Union peacekeepers will be deployed to eastern Chad later this month or early next year.
An EU force of up to 3,700 soldiers, half of them French, is due to start operations in the border region with Sudan on a UN mission to protect hundreds of thousands of refugees and the aid workers caring for them.
Morin said: "We hope the deployment of soldiers will be able to happen at the end of the year or the start of next year."
"We are making progress on the common financing, we're also making progress because Italy is going to provide the hospital structure. There are still a number of issues to be resolved such as air mobility, by which I mean helicopters."
Henri Bentegeat, head of the EU's military committee, said last month the planned force lacked 10 helicopters, a third medical facility and other support assets.
"Europe has been asked to guarantee this mission. It is up to the Europeans to fulfil their obligations. It is a question of credibility for the Europeans," Morin said.