The Association of Mineworkers and Construction Union (AMCU) was also optimistic the five-month stoppage that has crippled mine output could be nearing an end.
About 70,000 AMCU members downed tools in January at [DATA IMP:Impala Platinum], [DATA AMS:Anglo American Platinum] and [DATA LON:Lonmin Plc] , cutting 40 per cent of global production of the precious metal used for emissions-capping catalytic converters in automobiles.
Ramatlhodi's task team, charged with resolving the longest strike in South African mining history, was due to sit down with the management of the three platinum firms on Wednesday, a day after meeting AMCU leaders.
(READ MORE: Striking S.African mine union considers govt wage proposal)
"We are hoping to have it (strike) end by the end of this week," Ramatlhodi told Reuters. "It’s a work in progress, but so far so good."
Earlier, AMCU President Joseph Mathunjwa said the latest round of talks "went well", while a newspaper reported the union had agreed to a government wage proposal.
Business Report newspaper, citing an unnamed source close to the government negotiating team, said AMCU had accepted a wage hike slightly less than its current "living wage" demand.
The union wants 12,500 rand a month as a basic minimum wage to be achieved in four years.
The companies have offered pay increases of up to 10 per cent, which would raise the overall minimum pay package to 12,500 rand by July 2017, although this includes cash allowances for necessities such as housing.
Impala Platinum spokesman Johan Theron said the companies were ready to respond to the government recommendations, but did not provide any details.
Ramatlhodi said he was hoping to get the union and the companies around the negotiation table by the end of Thursday after meeting with them separately.
Ramatlhodi has been praised by the hardline union for his readiness to resolve the strike in his first week in office after numerous rounds of talks fell apart.
"Attitudes have hardened because of the length of the strike but slowly we are moving forward," Ramatlhodi said.