Earlier in the day, the mine's owner ArcelorMittal Temirtau said the death toll had risen to 28. As many as 208 of the 252 miners were evacuated to the surface, 18 of whom required medical assistance.
"Thirty-two bodies found, the search for 14 miners continues," the ministry said in a statement.
Karaganda Governor Ermaganbet Bulekpayev told a news briefing that the initial findings pointed to a fire that triggered a methane explosion. He said the blast was so powerful that it knocked out communication systems in a 1.2-mile radius.
An ad hoc government commission and the prosecutor general's office have opened investigations into the tragedy. The Kazakh president also ordered a halt in investment cooperation with ArcelorMittal Temirtau, which reported a deadly fire at another mine in August.
The Kazakh presidency has declared Sunday a national day of mourning. Russian President Vladimir Putin offered condolences to his Kazakh counterpart, Kassym-Jomart Tokayev, over the deadly accident, the Kremlin said.