A statement issued by the government on Tuesday said restrictions had been put on the movement of people and vehicles and on the media in the eastern border regions of Ouaddai and Wadi Fira and in the northern region known as the BET.
The clashes have been between ethnic Tamas and Zaghawas.
Deby and many members of his entourage are Zaghawas, but Mahamat Nour Abdelkerim, his new defence minister, is a Tama.
On Monday Abdelkerim accused Zaghawas of attacking Tamas. He said that hundreds of people have died from starvation and fighting in Dar Tama, while their cattle had been stolen.
EU peacekeeping
Earlier on Tuesday the head of the UN's refugee agency welcomed an EU decision to send 3,000 peacekeepers to eastern Chad, saying it would contribute to efforts to help civilians trying to escape the violence in neighbouring Sudan.
"It is a key instrument to allow for the security of the refugees ... and for the possibility of a more effective humanitarian operation," Antonio Guterres said.
On Monday EU foreign ministers gave their final approval for the deployment of European troops to areas of Chad and the Central African Republic which border Sudan's Darfur region.