JOHANNESBURG — Striking construction workers at 2010 World Cup stadiums have rejected an improved wage offer by employers, a union official said on Tuesday.

National Union of Mineworkers negotiator Bhekani Ngcobo said workers will not accept an 11.5 percent raise offered by employers, but says the union has lowered its demand for an increase to 12 percent from 13 percent.

The strike, which began Wednesday, is threatening to derail already tight schedules for construction projects across South Africa that are supposed to be completed by December for next summer's World Cup.

The union's Ngcobo said "the strike is still on" but that he hopes an agreement will be reached at a meeting with employers and mediators Tuesday.

At Soccer City near Soweto, a couple hundred protesting workers marched around the stadium, brandishing sharpened sticks and singing a Xhosa-language song that was a lament about how hard they worked but how little they made.

Soccer City is the venue where the World Cup finals will be held, and the stadium, which looks like a rust-colored calabash cooking pot, is already an architectural icon of the tournament.

In the shadow of the unfinished stadium there was confusion about the union's move to lower their demands and anger over pay that many say is below a living wage.

Monty Mokhine, who works as a supervisor, said he didn't believe the union would reduce their demands to a 12 percent pay increase.

"They must get a mandate from the people," he said.

The workers said that they were proud of their role in building a piece of South African history, but had little to show for their work.

"If I take my children here and say 'I've built that stadium,' they will not believe you, because you have nothing," said David Mahlangu, a laborer.

Victoria Noki, a casual laborer and single mother of three, said that her monthly salary was the equivalent of about $100 per month. Workers said they earn on average about $240 a month including overtime.

If workers do not see a wage increase and better working conditions, there would be a lot of unfinished stadiums in South Africa next year, she said.

"If you want it to be 2010, help us. Otherwise, you won't see it," Noki said. "It will be 2011."