Three of South Africa's biggest mines came to a standstill on Wednesday as wildcat strikes spurred by a police massacre and firebrand politician threatened to paralyse the industry.

A walkout at the Lonmin platinum mine in Marikana, where 34 workers were gunned down by police last month, showed no sign of relenting, with the company reporting attendance down to 1.8% at all its shafts.

The unrest continued to spread elsewhere as security guards fired teargas at strikers at Gold Fields' KDC west gold mine, near Carletonville, where 85% of the workforce downed tools. The company said the workers had been intimidating and threatening contractors.

The world's top platinum producer was also hit. A column of 1,500 marchers, chanting and waving sticks, confronted riot police backed by armoured vehicles in a tense stand-off at Anglo American Platinum's Bathopele shaft. The company said it had to redirect its staff from the premises for their own safety.

The mining sector, which accounts for a fifth of South African gross domestic product, has been in turmoil since the strike at Marikana last month which led to the deaths of 44 people, including police and security guards.

On Tuesday, near the area where miners were striking, another, unidentified, body was found with deep cuts in the back of the neck.

The flames have been fanned by Julius Malema, a former youth leader who was expelled from the governing African National Congress for ill discipline this year.

ANC officials and unions have accused him of exploiting the situation at the mines so as to revive his career, but Malema's ferocious anti-elite rhetoric has struck a chord with angry miners who feel betrayed by the government. Malema has toured mines making soapbox speeches and urging a national strike.

In an interview on South Africa's Talk Radio 702 on Wednesday, Malema said: "We are calling for mine change in South Africa. We want the mines nationalised. We want the workers paid a living wage … and somebody has to listen.

"Maybe this call has been ridiculed … by the authorities and mining bosses. Now we want to show them that we mean business. We are going to be engaging in very peaceful yet radical and militant action that will hit straight into the pockets of white monopoly capital."

Malema, who is facing an official investigation into corruption, widened his campaign on Wednesday by addressing disgruntled members of the South African army, prompting the country's military bases to be placed on high alert for the first time since the advent of democracy in 1994.

Nosiviwe Mapisa-Nqakula, the defence minister, accused him of trying to "mobilise against the state".

Speaking to about 60 soldiers in civilian clothes at a recreation centre south of Johannesburg, Malema said he would never conspire to overthrow the government through undemocratic means, but told his audience to mobilise in a disciplined way to save their jobs.

He condemned the president, Jacob Zuma, for treating them as a low priority and he drew attention to the president's polygamous lifestyle.

He said: "I don't know what is a priority to him, maybe getting married every year. He specialises on that one. Maybe that is what is going right for him.

"Here, children don't have books, people in hospitals don't have the necessary machines, they don't have roads or clean water.

"No one is above the law, not the military, not the presidency, and not parliament. Every court decision must be respected. We must respect the courts, but the leadership of this banana republic disrespects the courts."

Malema led the crowd in an alternative version of the struggle song that led to a court action against him for hate speech. Instead of the lyric Shoot the Boer, he settled for Kiss the Boer.

In another flash of humour Malema tweeted: "Defence Minister & Mr Zuma can remove the SANDF on high-alert now. We are finished with the mtng and there is no mutiny & no coup de tat."

Meanwhile, at Anglo American Platinum's Bathopele shaft protesters jeered fellow workers inside the plant.

One man, who did not wish to be named, told Reuters: "We are here to say to the men that work here that you must join us in the strike. We are not here to fight."

Anglo American Platinum said some operations had been halted by what it described as "widespread cases of intimidation". It claimed that many of the protesters were not its employees but members of neighbouring communities.

Evans Ramokga, a workers' leader, threatened to stop production in the entire platinum belt around the city of Rustenburg. "On Thursday we are going to combine efforts with the striking comrades at Lonmin mines," he told South African media. "We want to assure you that by Monday next week there will be no mining operation in Rustenburg."

Four Anglo American Platinum mines near Rustenburg employ more than 19,000 people, but have come under pressure since a collapse in platinum prices in the wake of the 2008 financial crisis.

South Africa is home to 80% of known reserves of platinum, which is used in jewellery and vehicle catalytic converters. The platinum price has gained nearly 20% since the shootings at Marikana, the worst security incident since the end of apartheid in 1994.

The strikes, which stem from a challenge by the small but militant Association of Mineworkers and Construction Union (AMCU) to the dominance of the ANC-affiliated National Union of Mineworkers (NUM), are also infecting the gold sector.

The NUM said workers at the Beatrix mine, run by Gold Fields, were set to strike this week, compounding industrial action already underway by 15,000 workers at the company's KDC West mine west of Johannesburg.

Malema has appeared twice at KDC to speak to striking workers and call for a monthly, five-day, national shutdown and the removal of the NUM's president.

His messages typically point to a narrow elite that has benefited in the 18 years since the end of racial apartheid but failed to deliver jobs and services to the majority. In one refrain, he said: "They have been stealing this gold from you. Now it's your turn."

The shootings at Marikana, and the government's inability to resolve the unrest, is also giving fresh impetus to a campaign to unseat Zuma at internal ANC elections in December. Malema has repeatedly called for him to stand down.