The airport said there were survivors and emergency services were working at the site.
The plane was heading to Nur-Sultan, formerly known as Astana, the nation's capital city.
The Bek Air jet, identified as a 23-year-old Fokker 100, hit a concrete wall and a two-story building soon after departing from Almaty, Kazakhstan's largest city and former capital, airport officials said. Everything was like in a movie: "screaming, shouting, people crying", she said.
The death toll was originally declared at 15 or more by local health authorities but was later revised to 12.
"Before crashing, the aircraft touched the runway with its tail twice, the gear was retracted", Sklyar said. It lost attitude at 7:22 a.m. local time, the Almaty International Airport said. There were 98 people onboard; initial reports indicate that at least 12 of them have not survived the accident.
No explanation for the crash has been given by the authorities, although the area was thick with fog when the plane went down.
Passenger Gulnara Koshenova said she heard screams before someone opened the emergency exit and everyone ran out.
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The plane crashed near Kazakhstan's Almaty airport.
"But Dana wanted to celebrate the New Year with her parents in Nur-Sultan and made a decision to take this flight".
A view of the site of a passenger plane crash outside Almaty.
In March, a Bek Air Fokker-100 plane with 116 passengers made an emergency landing at the capital's worldwide airport after its landing gear failed to deploy.
Kazakhstan's air safety record is far from spotless.
Russian President Vladimir Putin sent a message expressing his condolences to Kazakh President Kassym-Jomart Tokayev on Friday, saying Russia shares in the sorrow of those who have lost loved ones, and hopes for the speedy recovery of any survivors who were injured.
The Kazakh government said the crashed plane was produced in 1996 and its most recent flight certificate was issued in May 2019.