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"All the parties demonstrated willingness and resolved to see a quick and lasting resolution to this problem," she said in a statement.
"They also want to see the country healed from recent tragic events and for all of us to move forward together, and may our people find peace and solace in the efforts that we all are making in resolving the current impasse."
The meeting was held in the Rustenburg civic centre.
It brought together the National Union of Mineworkers, the Association of Mineworkers and Construction Union, Solidarity, the United Association Of SA, the Federation of Unions of SA, the National Council Of Trade Unions, the Congress of SA Trade Unions, and Lonmin management.
The minister said everyone agreed that "urgent steps" had to be taken to facilitate peace after 34 mineworkers were shot dead and 78 were wounded during a clash with police at the platinum miner's operation in Marikana, North West, last Thursday. Ten people, including two police officers and two security guards, were killed in the week preceding the clash.
The parties agreed they would conclude a peace accord by Wednesday. They would also start discussing the demands raised by the workers and how they could be accommodated within the existing collective bargaining arrangements.
Earlier, Lonmin [JSE:LON] said it was working towards peace with the strikers.
"We can confirm that we are working towards an agreement on peace," spokeswoman Sue Vey said.
"We are discussing the demands. It is a process, and it hasn't been finalised yet."
