Should the gold-miners strike go ahead, it would be the first country-wide strike in the world's biggest gold-producing nation in 18 years.
A strike would lead to the loss of around 28,000 ounces of gold production and 79 million rand ($12.21 million) in revenue per day, a Deutsche Securities analyst says.
NUM spokesman Moferefere Lekorotsoana said on Friday that the meeting, which took place at the NUM offices in Johannesburg, excluded both sides' negotiators from earlier failed wage talks as it was an informal gathering.
"When the CEOs feel they have an issue to raise during such a crisis, they go to the president," Lekorotsoana said.
"When the bosses come to our office, you know there is a problem," he said, adding that nothing concrete had come out of the meeting with NUM president Senzeni Zokwana.
Lekorotsoana declined to say which chief executive officers were at the meeting.
Another union official said the world's Number 2 producer, AngloGold Ashanti, had made an informal and improved wage offer to unions.
"AngloGold has made a new informal offer, but we are not responding to it yet. We want it to go through the formal channel, which is the Chamber of Mines. It's an improved offer," said the source.
AngloGold officials were not available for comment.
Lekorotsoana said he was not aware of the new offer.
Two years ago, unions declared a strike but it was averted hours before it was due to start with a last-minute deal.
"When the bosses come to our office, you know there is a problem"
president South Africa's National Union of Mineworkers
A strike would paralyse the South African mines of AngloGold, fourth-ranked Gold Fields and sixth-placed Harmony Gold and South Deep, a joint venture of South Africa's Western Areas and Canada's Placer Dome.
Gold Fields Chief Executive Officer Ian Cockerill said on Thursday that he hoped last-minute talks with unions could avert the strike.
Cockerill said the two sides were communicating despite the strike declaration.
The Chamber of Mines had earlier said informal last-minute talks between individual gold-mining firms and unions were under way in an effort to avert the strike.
"There's been no further developments; there are informal discussions continuing, I suppose even between individual companies and unions," said Frans Barker, chief negotiator for the Chamber of Mines.
"I'm afraid there has been no specific movement, though. The discussions will go on throughout the weekend. The strike would be very damaging to everyone, so all are trying to avoid it."
The unions called the strike after rejecting the latest offer by the Chamber of Mines, an industry group that negotiates on behalf of gold firms, of a 4.5% to 5.0% wage rise plus bonus payments.
Unions demand 12%
Unions are demanding a 12% increase.
Barker said around 100,000 gold miners in the sector are represented by three unions, with 80,000 belonging to the NUM.
The United Association of South Africa, representing around 15,000 members, said it was yet to make a formal stand, but that with about 90% of strike ballots cast by its members, most had voted to join the other two unions.
A strike could result in a loss of
more than $12 million a day
"Most members at this point have indicated they want to be part of the strike, but we have to wait for Monday for the formal result," said Tim Kruger, general manager in charge of the minerals and resources division at UASA.
Kruger said the union, which mainly represents supervisory and skilled artisans, would have to give a 48-hour strike notice should it decide on Monday to join the strike.
The gold producers have said the bonus offered as part of the talks would kick in if the domestic gold price rose above the current 90,000 rand per kg, adding 1% to wages for each 5000 rand per kg above the benchmark.
Mining firms, which gave workers a 10% wage rise two years ago, have taken a tough stand, saying they cannot afford rises much above inflation, which is running below 4%.