Workers have been striking for a week, paralysing work on 2010 World Cup football stadiums and on the mass transit Gautrain high-speed rail project which serves the area around Johannesburg.
The strike has raised concerns about whether South Africa will be ready for the tournament and hit shares in some major construction companies.
It also comes as unions threaten strikes in a number of other sectors important to South Africa's economy, including gold.
NUM earlier said workers and employers had agreed on a 12 per cent wage increase, but were still arguing over efforts by companies to ban any further strikes until after the showcase football tournament.
The union initially demanded 13 per cent increase.
Matosa declined to comment on what level of wage increase had been agreed and on whether the workers would be blocked from further industrial action until after next year's event.
"Those details will be revealed after the signing," he said.
The strike threats have increased pressure on Jacob Zuma, South Africa's new president, who took office in May and found a good deal of support among the unions.
But in recent weeks the unions have demanded big wage increases and threatened strikes across several sectors. Zuma, battling the country's first recession in 17 years, has little room for manoeuvre given the lacklustre economy.
Companies, too, are fighting a slump in demand and are under pressure from shareholders to curtail costs.
Unions announced strikes in the energy, chemical and paper industries on Tuesday and said action in the important gold sector was "highly likely".