JOHANNESBURG, Sept 13 (Reuters) - Lonmin Plc said on Thursday it had made an offer to striking workers at its South African operations, after four weeks of widening labour unrest that has threatened mining output in Africa's biggest economy. "Following negotiations today, Lonmin has presented an offer," to representatives of the workers, the company said in a statement, adding that negotiations would continue on Friday. The world's third-largest platinum miner also said the talks included "all parties", a sign that the militant AMCU union - which has been a driving force in the labour unrest - was now involved. Lonmin last week signed a "peace accord" with some of its unions, but that deal did not include the breakaway Association of Mineworkers and Construction Union (AMCU). AMCU is calling for hefty pay hikes and challenging the long dominance of the government-affiliated National Union of Mineworkers. The wave of strikes has engulfed other mining companies, including top platinum producer Anglo American Platinum and gold producer Gold Fields. Last month police shot dead 34 striking miners at Lonmin's Marikana mine, the bloodiest security incident since the end of apartheid in 1994.