The flight was carrying 93 passengers and five crew members.
A survivor of the crash described the terror aboard.
Conflicting reports remain regarding the number of casualties, with medics reporting 15 dead, while the internal affairs ministry puts the figure at 12, including the plane's captain, Marat Muratbaev.
The reports said Kasakh aviation authorities have grounded all Fokker 100 jets in the country following the crash. It reportedly "lost altitude during takeoff and broke through a concrete fence" before hitting a two-story building, Kazakhstan's Civil Aviation Committee said in a statement. There was no fire upon impact.
One survivor, businessman Aslan Nazaraliyev, told the BBC that the plane had begun vibrating violently.
He said most of the passengers who died or suffered serious injuries had been in the front part of the plane. He and others managed to get out and helped fellow passengers to safety.
"It was ugly. It was dark".
"Astana 671, we do not know where the Fokker 100 is located", the dispatcher said.
Eight of the victims died at the scene of the disaster, two while receiving medical attention at the airport and two in hospital. Ten adults are said to be in a critical condition.
Several foreign nationals, including two Ukrainians, one citizen of Kyrgyzstan and one Chinese national were on board the plane.
Among those killed was Dana Kruglova, the executive editor of the website Informburo.kz, the emergency committee announced.
The cause of the crash in the Central Asian nation was unclear, but authorities were looking at whether pilot error or technical failure were factors, Kazakhstan's deputy prime minister Roman Sklyar said.
At the airport at Nur-Sultan, relatives of the passengers - some of whom were going to join their families for the holidays - were being briefed on their fate and offered flights to Almaty. In a post, the site said Kruglova was travelling from Almaty to the capital, Nur-Sultan, to celebrate the New Year holiday with her parents.