* 14-week strike to continue
* Companies urge workers by text message to take offer
* Tensions high on restive platinum belt (Adds background, details)
By Zandi Shabalala
MARIKANA, South Africa, April 29 (Reuters) - Members of South Africa's striking mining union AMCU have rejected the latest wage offer from the world's top three platinum producers, its president said on Tuesday, extending a crippling 14-week stoppage.
"The members have rejected the offer from the employer," Joseph Mathunjwa told reporters after addressing a rally of workers near Lonmin's Marikana mine.
The Association of Mineworkers and Construction Union (AMCU) held similar rallies in recent days at Anglo American Platinum and Impala Platinum.
It now plans to meet this week with the companies to inform them in person of the rejection, Mathunjwa said.
Marathon wage talks collapsed last week, dashing hopes for an imminent end to South Africa's longest and most costly mining strike, which has hit 40 percent of global platinum production and threatens growth in Africa's most advanced economy.
The companies say they are taking their offer directly to the workers via cellphone text messages and radio and newspaper spots in a bid to circumvent AMCU's leadership, setting the stage for a grinding showdown between capital and labour.
Their bet is that after three straight months with no pay, the rank and file will to stay off the job has been sapped.
Initially AMCU demanded an immediate doubling of the basic wage - net salary before allowances such as housing - for entry-level workers to 12,500 rand ($1,200) a month.
The union has since said it would accept annual increases that would reach this goal in three or four years' time.
The producers' latest offer, made last Thursday, was for wage rises of up to 10 percent and other increases that would take the minimum pay package - the basic wage including the allowances - to 12,500 rand a month by July 2017.
Companies say they cannot afford any more given rising costs and depressed prices for the precious metal used for emissions-capping catalytic converters in automobiles.
Underlining this point is the muted price reaction to the stoppage despite the over 700,000 ounces of production lost to it so far - around 12 percent of global annual output.
Spot platinum is fetching around $1,412 an ounce, around 2.5 percent lower than it was on the eve of the strike.
Industry sources maintain AMCU's militant core is using intimidation to keep members in line and say most of its workers have returned to their home villages far from the shafts, so its mass rallies are not a real indication of its support.
Mathunjwa dismissed this, telling reporters on Tuesday that "as you can see, all our members are here in full force."
Tuesday's rally was attended by around 5,000 AMCU activists but it was not possible to say if they all belonged to Lonmin. The union has around 70,000 members on the platinum belt.
Sue Vey, a spokeswoman for Lonmin, said "a lot" of its workers had indicated by text message they wanted to take the offer and return to work but exact numbers would not be compiled before the end of the week or early next week.
She said workers could sign an "intention form" at company premises or the offices of TEBA, a mine recruitment agency with offices in regions from where much of the mine labour force hails, such as rural parts of the Eastern Cape province.
This could undermine AMCU as it is not clear how far its reach and influence extends beyond the platinum belt.
A painful restructuring is considered likely after the dust clears from the strike, with job losses expected, especially around Amplats' struggling Rustenburg operations, which it has signaled it could sell or mothball.
This makes the strike a headache for President Jacob Zuma and the ruling African National Congress Party (ANC) with a general election looming on May 7.
AMCU's dominance in the platinum belt has a political dimension anyway, as it emerged as the top labour group in the sector in 2012 after poaching tens of thousands of members from the National Union of Mineworkers (NUM), a key ANC ally, in a vicious turf war that killed dozens of people.
Tensions remain high, underscored by an outbreak of violence in the area on Sunday when the sports minister and NUM officials were campaigning for the ANC.
$1 = 10.6193 South African Rand Reporting by Zandi Shabalala; Writing by Ed Stoddard; Editing by Joe Brock and Mark Potter