Lonmin management was speaking to the representatives of striking workers at Marikana on Tuesday night, the Bench Marks Foundation said.
"Information on the outcome of the meeting will be made available once the meeting has concluded," said the foundation's chairman Bishop Jo Seoka, who is also president of the SA Council of Churches.
The meeting was to have been held at the Lutheran Church, in Wonderkop, but the venue was changed after Lonmin management raised concerns about security, he said.
"Another venue was found and the meeting has convened."
Police opened fire on a group of protesting workers gathered on a hill near the mine on Thursday, killing 34 of them and wounding 78. Another 260 were arrested on charges of public violence and remain in custody.
In the week leading up to the shooting, 10 people — including two police officers and two security guards — were killed.
The protests were believed to be linked to rivalry between the National Union of Mineworkers and the Association of Mineworkers and Construction Union over recognition agreements at the mine. Workers also wanted higher wages.
"It is our hope that an agreement can be reached by all involved which will end this very sad situation. Too many lives have been lost already," said Seoka.
The faith-based organisation said that by not entering into negotiations with the workers, Lonmin had to bear a heavy burden of responsibility for the escalation of the conflict and the deaths.