"Our members are victimised each and every day," Congress of SA Trade Unions (Cosatu) Gauteng secretary Dumisani Dakile told reporters in Johannesburg.
Dakile said Cosatu was concerned about security in the area and called on the State Security Minister Siyabonga Cwele to ensure the situation was under control.
"They must be able to deploy all necessary resources to make sure that particular area remains calm and no one is injured and no one is killed..."
Operations at the platinum mine were suspended on Tuesday morning.
"We can confirm there is a stoppage. Workers arrived for work, but did not go underground," said spokesperson Sue Vey.
Workers are demanding that the local office of the National Union of Mineworkers (NUM) be shut down.
The wildcat strike will continue until NUM's office has been shut down, the Association of Mineworkers and Construction Union (Amcu) said.
"The employer refused to close the NUM office, saying NUM had been given notice to vacate offices by July 3," said branch chairperson Mceli Balimani.
One of the workers, Jerry Lintle said workers wanted the NUM out of Lonmin.
"They are no longer the union of choice. They must give Amcu space to operate," he said.
Tense situation
Earlier, NUM regional co-ordinator Mxhasi Sithethi said the situation was tense at the mine.
"People are singing outside our office, demanding the closure of the NUM office..."
The NUM and Amcu have been fighting for control of the mines in the area since last year.
Tuesday's strike followed the death of Amcu regional organiser Mawethu Steven, who was shot dead in Photsaneng, in the Nkaneng informal settlement, on Saturday.
An NUM shop steward and his twin brother were also shot dead in Nkaneng on Saturday.
On Monday, Amcu president Joseph Mathunjwa appealed for "calm" in the platinum belt following the shooting.
"We would like to call on all our members during this difficult and emotional time to remain calm and allow the law to take its course," he said.
On August 16, police shot dead 34 striking miners while trying to disperse them at Wonderkop. Another 10 people were killed in strike-related violence the week before.