Yanakiwa Mining said in a statement that 175 miners were safely evacuated after the accident on Friday evening.
The company said 27 of the dead worked for a mining contractor.
Government officials said an investigation was underway into the cause of the fire.
Some news reports said preliminary investigations indicated the possibility of an explosion due to an electrical short in part of the mine at a depth of 100 meters below the surface.
The relatives of the victims were taken by bus to the Yanakiwa mine, in the Arequipa region, where they were briefed by security personnel.
Some sat in front of posters at the entrance to the mine, waiting for the bodies of their loved ones.
Marcelina Aguirre said her husband was among the dead, noting that he told her there were dangers in the mine.
“We are very worried, very sad, because we are losing a husband who left behind two children,” Aguirre added.
For his part, the attorney general of the financial district of Arequipa said that the investigators were working to clarify what happened.
“During the investigation, the prosecution will determine the cause of the tragic incident and the responsibilities of those involved,” its statement said.
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