Chadian troops have deployed on their border after a clash with Sudan forces.
The Arab militia are accused of ethnic cleansing in Sudan
A Chadian government spokesman said the troops would protect local civilians and refugees from the Darfur region of Sudan who are sheltering in the area.
The clash is the first to involve army troops since Sudanese civilians began fleeing into Chad a year ago.
The incident occurred after Arab militia staged a cross-border raid in Chad. Chad troops pursued them until they encountered Sudanese forces.
The United Nations estimates that 10,000 people have died in the conflict and one million have fled their homes in Darfur.
More than 100,000 people have crossed into Chad, but militia raids have targeted refugees across the border.
The United Nations plans to move the refugees away from the border to safer areas, but UN agencies have been slow to transfer the refugees who remain vulnerable and desperately in need of humanitarian assistance.
Chadian official Allami Ahmat, who helped to negotiate a ceasefire in the conflict in the western Sudanese region of Darfur earlier this month, said the incident was proof that the Janjaweed militia had not been disarmed as promised by the Sudanese government delegation at the peace talks.
"This situation is all the more unacceptable because the Sudanese army tolerates and offers land and air backup to the Janjaweed militias," he said.
The UN has accused Sudan of backing Arab militias in a campaign of "ethnic cleansing" against black residents in Darfur.
During a visit to Al-Fashir in Darfur earlier this week, President Omar Hassan al-Bashir said peace had been restored to the region.
Two rebel groups in Darfur took up arms last year, accusing the government of ignoring the region.
However, recent reports blame rebels in Darfur for an attack on a humanitarian aid convoy in the region and for the killing of a local chief.
A United Nations human rights team is in Darfur, investigating claims of atrocities.