More than 200 000 National Union of Metalworkers of South Africa (Numsa) members downed tools on Tuesday last week, demanding wage increases of between 12-15%.
The strike dealt a further blow to the country's economy, coming just two weeks after miners in the key platinum sector agreed a slightly higher wage deal to settle a five-month stoppage.
Ngobese said: "If the employers can present something that we strongly feel we can take back to our members for a mandate, we will gladly do that, but in the absence of that, the strike continues."
Ngobese said the union had not received a revised offer.
The Steel and Engineering Industry Federation of Southern Africa said last week that Numsa had rejected its 10% offer.
Employers and labour representatives met government officials on Monday as Pretoria intervened to try and break the deadlock costing the country's metals industry - which has shed hundreds of thousands of jobs the past decade - an estimated R300m a day.
The union is also demanding that any pay agreements apply for a year only while companies want a three-year deal.
The strike has hit components factories supplying General Motors' South African plant, but the US auto maker said it had sufficient inventory for both domestic and export customers for the medium term.
"The strike in the metal and engineering sector has impacted upon supply of components to our production line, resulting in our line not being operational since July 3," said GM spokesperson Denise Van Huyssteen.
"To date we have lost three days of production."
German counterpart BMW brought forward a week of a pre-planned annual plant shutdown for maintenance last week, spokesperson Guy Kilfoil said.
"We were going to close the plant at some point during the year for maintenance anyway. We just brought it forward because we knew the strike was coming," Kilfoil said, adding the factory would reopen on Tuesday.
Compatriot Mercedes Benz said there had been no impact so far at its local operations, while Toyota said it was still at "full production".
Separately, about 2 000 miners affiliated to the National Union of Mineworkers (NUM) remained on strike at Impala Platinum's Marula mine on Monday, Implat's spokesperson Johan Theron said.
Implats, the world's second largest producer of platinum, and rivals Anglo American Platinum and Lonmin are still reeling from the five-month strike that ended in late June.
That stoppage was led by NUM's rival, the Association of Mineworkers and Construction Union (Amcu), which eventually settled for wage hikes of up to around 20%.
The Marula operation was not hit by that strike as its NUM-affiliated workforce signed a wage deal last year.
But Theron said on Friday that it seemed the Marula miners now wanted the same wage deal that Amcu had obtained for its members at other Implats mines.