The plane was travelling from Almaty to the Kazakh capital Nur-Sultan.
Almaty airport authorities said that personnel from emergency services were working to rescue the survivors.
"Those responsible will face tough punishment in accordance with the law", Kazakh President Kassym-Jomart Tokayev tweeted, expressing condolences to the victims and their families.
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The airplane lost attitude at 7:22am, Almaty International Airport said.
Almaty's airport said it was operating normally and the flight schedule was unaffected. Footage from the site, which was cordoned off, appeared to show the Fokker 100 plane had hit a building. The plane's tail twice touched the runway as it was taking off, Sklyar said, according to Russia's Tass state news agency.
The Ministry of Industry also said that the plane's flight recorders would be passed on to the Interstate Aviation Committee in Moscow for examination and analysis.
The Bek Air plane was flying from Almaty - Kazakhstan's largest city - to the capital Nur-Sultan when it smashed into a building just after take-off.
The year before that, 27 people died when a military plane carrying Kazakh security officials crashed in the country's south.
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Officials ruled out weather-related issues, saying that the airport runway was in flawless condition and that the plane had been treated with an anti-icing agent.
In Almaty, dozens of people lined up in front of a local blood bank to donate blood for the injured.
The authorities were investigating pilot error or technical problems as possible causes of the crash, Deputy Prime Minister Roman Sklyar said.
Authorities quickly suspended all Bek Air and Fokker 100 flights in Kazakhstan while the investigation got underway.
The Fokker aircraft had 100 passengers and crew on board.
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Ensminger Jr.is the son of Steve Ensminger , who is the offensive coordinator for the LSU football team. The smoldering remains of the plane were resting in a field near the post office.
The ASN said the airline was added to the European Union's list of banned air carriers in 2008 but was removed in December, 2016.