A strike leader told thousands of workers to continue the strike on Wednesday. Workers told a Reuters reporter no one would show up for the night shift.
Activists also said they would go to shafts to threaten those who showed up for work, using the Zulu word for "rat" to describe them.
Sapa reported Congress of SA Trade Unions (Cosatu) urging law enforcement agencies to prioritise security in the area surrounding Lonmin.
"Our members are victimised each and every day," said Cosatu Gauteng secretary Dumisani Dakile.
He 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..."
Killings condemned
Police Minister Nathi Mthethwa said there was a reinforcement of police in the area.
"We are monitoring the situation and urge the strikers to refrain from carrying any dangerous weapons, publicly, because that is against the law," he said in a statement
"We... call upon all in society to uphold the law because as government we shall not tolerate any massacre or intimidation of any law abiding citizen."
The platinum belt towns of Rustenburg and Marikana, which saw violent strikes at Lonmin and other producers last year, are a flashpoint of labour strife, with tensions running high over looming job cuts and wage talks.
Aggravating the situation is a turf war between the Association of Mineworkers and Construction Union (Amcu) and the National Union of Mineworkers (NUM).
An NUM spokesperson said Tuesday's strike appeared to stem from anger over the killing of an Amcu member. A police statement said a 46-year-old man "alleged to be the regional organiser of Amcu" had been shot dead in a Rustenburg tavern on Saturday.
Down with NUM
The striking workers marched to the rocky outcrop near the Marikana mine where 34 strikers were shot dead by police in August last year and were then taken by bus to the stadium, an indication the strike had been planned.
Many chanted: "Down with NUM, we will destroy it today."
The protesters said they were demanding the closure of the NUM offices at Lonmin, which said last week that Amcu now represented over 70% of its workforce.
The strike puts pressure on President Jacob Zuma's ANC, which was criticised for its handling of last year's turmoil and faces accusations that it is neglecting the poor masses 19 years after the end of apartheid.
The mine unrest is rooted in glaring income disparities and low wages.
Jobs at risk
Lonmin spokesperson Sue Vey said all Marikana's 13 shafts were idle.
The company told the strikers to return to work. "Failure to do this could result in further reduction of jobs at Lonmin," it said in a memo to staff, a copy of which was seen by Reuters.
It said the strike action "will severely impact the viability of Lonmin and will put your work and the sustainability of your family at risk".
The stoppage occurred during Platinum Week, an annual gathering in London of industry executives and analysts.
Lonmin workers also downed tools for one day in March during a visit by media, embarrassing the company as it tried to show how it had recovered from last year's problems.
Acting chief executive Simon Scott told Reuters in an interview late on Monday the company would tell unions to curb expectations for forthcoming wage talks because it remains under pressure despite reporting robust first-half earnings.
"While the results are a significant improvement over last year, this is still not an industry that is making a lot of money. This is still not an industry that is giving shareholders a huge return," he said.
Social tensions in the area have been further stoked by plans by Anglo Platinum [JSE:AMS] (Amplats), the world's top producer, to slash 6 000 jobs in a bid to restore profits. That is less than half the 14 000 initially targeted but unions have still vowed to fight the lay-offs.