Pit gas is thought to have exploded in the coal mine run by Mittal Steel Temirtau in the Karaganda Region, southeast of the country's capital, Astana. A total of 374 people were working at the moment 620 meters (over 2,000 feet) deep. More than 300 miners managed to reach the surface after the blast.
"We have found 33 bodies, and the bodies of another eight miners who were in the pit at the time of the explosion have not been located yet," Zhanara Bekbanova said. "Unfortunately, we assume [the miners] are dead."
Rescue work has been obstructed by high gas levels and the high temperature in the mine.
The trade union of Mittal Steel Temirtau's coal arm pledged $12,000 in compensation to the families of late miners, and prosecutors said they had opened a case into negligence.
President Nursultan Nazarbayev offered his condolences to the late miners' families and ordered that a commission be set up to investigate the causes of the tragedy and to arrange assistance to the families.
"All Kazakhs empathize at this difficult time with the disaster that has struck the miners of Karaganda," a message from the president said.
The incident in Kazakhstan was not the only one Wednesday. In Ukraine, 13 people died following an explosion at a mine in the east of the country.
A total of 25 miners died after a blaze broke out September 7 in a Russian pit in southern Siberia.