* Platinum belt on edge after weekend killing

* Chanting miners march with sticks and branches

* Lonmin share price slides, day after positive results

* Tensions rooted in union turf war, income disparities (Adds details, Lonmin acting CEO, finance minister, pvs JOHANNESBURG)

By Joshua Nhlapo

MARIKANA, South Africa May 14 (Reuters) - South African workers of world No. 3 platinum producer Lonmin launched a wildcat strike on Tuesday, halting all of the company's mine operations and reigniting fears of deadly unrest that rocked the industry last year.

The platinum belt towns of Rustenburg and Marikana, which saw violent strikes at Lonmin and other platinum producers last year, are a flashpoint of labour strife with tensions running high over looming job cuts and wage talks.

Further complicating the picture is a turf war between the Association of Mineworkers and Construction Union (AMCU) and the National Union of Mineworkers (NUM) - a political ally of the ruling ANC, which has lost many of its members to the AMCU.

An NUM spokesman said Tuesday's strike appeared to stem from workers' anger over the weekend killing of an AMCU member. A police statement said that a 46-year-old man "alleged to be the regional organiser of AMCU" was killed in a Rustenburg tavern on Saturday when an assailant shot him four times with a 9mm pistol.

Hundreds of Lonmin workers, some carrying branches and sticks, chanting "Down with NUM, we will destroy it today", marched to the rocky outcrop near Lonmin's Marikana mine where 34 strikers were shot dead by police in August last year.

Miners told a Reuters reporter they were gathering to wait for their leaders to come and address them.

The share price of Lonmin slid almost 7 percent and the rand currency hit 3-week lows, as investors worried about a repeat of 2012's turmoil, which hammered platinum and gold production and triggered credit downgrades for Africa's largest economy.

"Peace and returning to normal production in our mining industry is absolutely critical to our economy so I'm hoping that everybody sits down together and solves their problem," South Africa's Finance Minister Pravin Gordhan said on Tuesday in Cape Town, reacting to the latest Lonmin stoppage.

It puts pressure on President Jacob Zuma's African National Congress (ANC), which was criticised last year for its handling of the situation and faces accusations that it is neglecting the nation's poor masses 19 years after the end of apartheid.

The mines unrest is rooted in glaring income disparities and low wages for a workforce that is largely semi-literate and drawn from poor rural areas of South Africa.

LONMIN URGING

Platinum's spot price rose 1.5 percent on news of the strike, widening its premium over gold to more than $60 an ounce, the highest in a month.

Lonmin spokeswoman Sue Vey said all 13 shafts at the company's facility were not working. She said there was no indication at this stage as to why employees were on strike.

The company told the strikers to return to their posts, adding their action could lead to job losses.

"We urge you to refrain from this unprotected (illegal) action and immediately return to work. Failure to do this could result in further reduction of jobs at Lonmin," it said in an internal memo to staff, a copy of which was obtained 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 Lonmin 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.

Lonmin's acting chief executive Simon Scott told Reuters in an interview late on Monday the company would tell unions to curb expectations of forthcoming wage talks, warning 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 American Platinum, 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 against the lay-offs.

Gideon du Plessis, deputy general secretary of the Solidarity trade union which represents skilled workers, said he understood AMCU was demanding the NUM close its office at Lonmin. AMCU represents over 70 percent of Lonmin's workforce.

Police said earlier they were monitoring the situation at Marikana.

(Additional reporting by Sherilee Lakmidas and Agnieszka Flak in Johannesburg, Wendell Roelf in Cape Town and Clara Ferreira-Marques in London; Writing by Ed Stoddard; Editing by Pascal Fletcher and Sophie Walker)