* Mineworkers union leader demands meeting with Zuma
* ANC deputy president says hard to tell what is going on
* Rand slides to four-year low against dollar
By Xola Potelwa
RUSTENBURG, South Africa, May 17 (Reuters) - The leader of South Africa's biggest platinum mining union threatened on Friday to bring Africa's No. 1 economy "to a standstill" and demanded a meeting with President Jacob Zuma, ramping up the rhetoric in an 18-month labour crisis.
The rand, which tumbled to a four-year low against the dollar on Thursday on fears of a strike at Anglo American Platinum (Amplats), extended its slide on concerns about further disruptions to an already struggling economy.
The currency fell as low as 9.4334, its lowest since April 2009 when emerging markets were still reeling from the effects of the global financial crisis.
Joseph Mathunjwa, head of the Association of Mineworkers and Construction Union (AMCU), said Zuma's ruling African National Congress (ANC) was ignoring violence against its members in the platinum belt near the northwest city of Rustenburg.
"We are going to write another last letter to the office of the president that we need a meeting in order to talk about these issues at Rustenburg, of the killing of our members," he said on Johannesburg's Talk Radio 702.
"This is the show of AMCU's commitment to peace," he said. "We said we are going to bring the economy to a standstill."
AMCU's emergence since early 2012 as the most powerful platinum union has turned mining labour relations on their head and sparked fears of a wave of worker militancy stretching from the car plants of Durban to the vineyards around Cape Town.
The crumbling of the decades-long monopoly of the National Union of Mineworkers (NUM) has also opened the door to an array of worker committees and anti-capitalist activists opposed to the ANC and South Africa's post-apartheid economic status quo.
Faced with such a diverse and novel range of forces, the ANC is running blind even though the decline of NUM - its ally in the decades-long anti-apartheid struggle - is likely to hurt it in an election next year.
"It's very difficult to decipher properly what is going on," ANC deputy president and NUM founder Cyril Ramaphosa told the radio broadcaster.
"There's union rivalry, fighting for turf, and there are obviously other elements coming into the space. We keep hearing about the Socialist Workers Party or whatever and that seems also to be fanning the flames," he said.
FEAR, LOATHING, CONFUSION
In Rustenburg, the heart of the platinum belt 120 km (70 miles) northwest of Johannesburg and home to 80 percent of known global platinum reserves, confusion is compounded by fear.
An AMCU organiser was shot dead at the weekend in a bar in Marikana, just miles from Rustenburg, where police killed 34 AMCU-linked Lonmin workers last August - the biggest loss of life at the hands of security forces since the end of apartheid in 1994.
AMCU members have also been implicated in the violence, including the killing with machetes of security guards and police last year.
In such a febrile atmosphere, Amplats announced plans last week to lay off 6,000 men to try to restore profits at the world's top producer of the precious metal.
However, a protest strike called for Friday by at least two AMCU officials failed to materialise as all workers reported for the morning shift as normal.
"There are too many parties and committees now so you don't know what's actually happening and who to believe," said Enoch Sonkwale, a 37-year-old train driver at Amplats' Khomanani shaft in Rustenburg.
Amplats shares gained more than 2 percent from Thursday's eight-year low.
However, there was no respite for the rand, which has now lost 10 percent against the dollar this year, a decline likely to stoke inflation and reduce the chances of the central bank rolling out a growth-boosting interest rate cut at a policy meeting next week.
"The recent currency move is likely to keep it (the central bank) on edge a little, especially because it is only the start of what is likely to turn out to be a long, fraught and violent strike season," Nomura analyst Peter Attard-Montalto said.