There was no official mention of survivors, but one witness reported seeing some people jump out of the aircraft before it crashed.
The Araban-language Algerian TV Dzair said five people were in a critical state but it was unclear if they had been inside the plane.
Several witnesses told Algerian TV network Ennahar they saw flames coming out of one of the planes' engines just before it took off.
"The plane started to rise before falling," an unidentified man lying on what seemed to be a hospital bed told Ennahar TV. "The plane crashed on its wing first and caught fire."
Video on the state-TV channel ENTV showed a blackened hulk broken into pieces, with huge wheels scattered about along with other plane parts. Firefighters doused the flames while body bags were placed in rows in the field.
A total of 257 people died in the crash, state TV reported.
A member of Algeria's ruling FLN party told the private Ennahar TV station the dead included 26 members of Polisario, an Algerian-backed group fighting for the independence of neighbouring Western Sahara – a territory also claimed by Morocco in a long-running dispute.
The plane was heading to Tindouf, an area on Algeria's border with Western Sahara, but crashed on the airport's perimeter, Algeria's Defence Ministry said.
Tindouf is home to thousands of refugees from the Western Sahara standoff, many of them Polisario supporters.
UN attempts to broker a settlement have failed for years in the vast desert area, which has contested since 1975 when Spanish colonial powers left. Morocco claimed the territory while Polisario established its self-declared Sahrawi Arab Democratic Republic there.
Algeria's defence ministry issued a statement expressing condolences to families of the victims.
In February 2014, an Algerian Air Force Lockheed C-130 Hercules crashed in a mountainous area in eastern Algeria killing 77 passengers and leaving one survivor.
- additional reporting AP
