The first flight, organized by the International Organization for Migrants, was scheduled to leave from the capital, Bangui, Saturday afternoon, CNN reported.
The charter flight will carry as many as 320 Chadians to their home country, said Francois Goemans, IOM's emergency coordinator for the operation. Two more flights will follow, returning a total of 1,000 people to Chad.
Two other flights will ferry Malian migrants out of the country, eventually evacuating 700 people.
IOM has helped evacuate thousands from Senegal and Burkina Faso in recent weeks.
The organization said it had also received requests for assistance from other countries including Sudan and the Democratic Republic of the Congo, the BBC reported.
Conditions endured by migrants hoping to leave the country are the worst he'd seen in 20 years, Goemans said.
"The situation is terrible," he told CNN+. "There's diarrhea, the sanitation is terrible."
Goemans added that "people are dealing with some strains that you cannot believe -- so many of their relatives have been killed ... and they are all traumatized."
The operation will likely take several weeks to evacuate all the migrants. Some 33,000 migrants still need help, the organization aid.
At least 1,000 people have died in CAR since fighting began in December, with a coalition of rebel groups forcing out President Francois Bozize. Interim President Michel Djotodia and his prime minister, Nicolas Tiangaye, resigned Friday at a regional summit in Chad.
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