* Police confirms four Lonmin workers were murdered
* Lonmin expects mass workers return this week
* Levels of policing will increase from May 14
* Implats conduct SMS vote on wage offer (adds police comments on four murders)
JOHANNESBURG/LONDON, May 12 (Reuters) - One South African miner was killed on Monday and three others died over the weekend in violence at strike-hit platinum mines, police said, threatening Lonmin hopes to end the dispute this week.
South Africa's longest and most costly strike ever has hit 40 percent of global platinum output and dented already sluggish growth in Africa's most advanced economy.
London-listed Lonmin hoped more miners would return to work this week after it made its wage offer directly to employees, sidestepping the majority Association of Mineworkers and Construction Union (AMCU) in a bid to end a four-month strike.
But violence related to labour disputes has escalated in the last few days in the North West province of South Africa, after the number of employees reporting for work started to increase.
Police Minister Nathi Mthethwa announced the deaths in a statement and added: "The protection of those involved in the labour disputes in the North West is a matter that government takes extremely seriously."
In a joint statement, platinum producers Lonmin, Amplats and Impala reported at least 20 assaults in the last two days and several serious incidents of intimidation against employees and bus operators driving them to the mines.
The police said after meetings with platinum producers and labour representatives on Friday that they would increase patrols along workers' commuting routes from May 14, the date that Lonmin hopes that striking mineworkers will return to work.
"The police will continue... to assure all parties that the protection of citizens will be at a high level and to seek ways to defuse tension," Mthethwa said.
The National Union of Mineworkers (NUM) and the Solidarity union, which mainly represents skilled workers, said their members returning to work were being intimidated.
"If Lonmin wants our members to return to work they have to guarantee their safety," said NUM spokesman Livhuwani Mammburu. "We have no faith in police - they are not doing anything to protect workers."
In 2012, Lonmin was at the centre of labour unrest and violence in South Africa that left dozens dead.
The producers also expressed alarm at AMCU warnings that "something else" could happen if producers continued engaging workers directly. AMCU was not immediately available to comment.
Lonmin, the smallest of the three platinum firms hit by the costliest strike in South African mining history, saw its earnings shrink in the six months to the end of March and posted a $164 million in strike-related costs.
Lonmin said it expected to assess the success of the return to work by the end of this month, with production provisionally scheduled to start in June, if successful.
Workers attendance levels rose 12 percent by last Friday, up from between 9 percent and 11.5 percent since the strike began, said Lerato Molebatsi, Lonmin head of public affairs.
London-based Investec analyst Marc Elliott said Lonmin would need extra security from the government to make workers feel safe enough to return. "Now with the elections out of the way hopefully the government can be more proactive," he said.
Lonmin said restructuring of its business and job cuts were inevitable as the strike had exacerbated already difficult market conditions.
WAGE OFFER VOTE
Lonmin's larger rivals, Anglo American Platinum and Impala Platinum, have also presented wage offers directly to employees after talks with the AMCU collapsed.
Implats spokesman Johan Theron said the company was due to conclude an SMS vote on its offer on Tuesday.
AMCU's leaders maintain that most of their roughly 70,000 striking members are not happy with the latest offer.
The companies are offering increases of up to 10 percent that they say would raise the overall minimum pay package to 12,500 rand ($1,200) a month by July 2017, including cash allowances such as for housing.
AMCU had initially demanded an immediate increase to 12,500 rand in the basic wage, excluding allowances, but softened that in March to staggered increases that would amount to 12,500 rand within three or four years - still a third more than what the companies are offering in basic salaries.
The strike highlights the discontent among black miners who feel they are still not reaping the benefits of the country's mineral wealth two decades after apartheid ended.
($1 = 10.3872 South African Rand) (Additional reporting by Zandi Shabalala and Tiisetso Motsoeneng in Johannesburg; Writing by Olivia Kumwenda-Mtambo; Editing by Ed Cropley and Tom Heneghan)