JOHANNESBURG (Reuters) - Thousands more workers at South African power stations plan to join a strike on Wednesday over pay at state-run utility Eskom, their union said on Tuesday.

The strike began on Monday when about 1,500 members of the National Union of Mineworkers (NUM) downed tools after wage talks stalled. Eskom branded the stoppage illegal because its members are prohibited by law from striking, but said its operations had not been affected so far.

The union said that all of its 15,000 members at the utility, or close to a third of Eskom's workforce, will stop work on Wednesday. Tuesday was a public holiday in South Africa.

"It is going to be a total withdrawal of labor by our members. NUM members will be striking for the right to strike at Eskom," the union said in a statement.

Eskom could not be reached for comment on how its operations would be affected on Wednesday.

Eskom said on Monday that arbitration over the wage dispute was continuing. The utility is offering pay hikes of 7 to 9 percent while NUM is looking for increases of 12 to 13 percent.

The labor dispute is the latest problem to beset cash-strapped Eskom, which has struggled to meet power demand in South Africa due to its aging power plants and grid. However, it has managed a year without rolling blackouts that have hurt the economy in the past.

(Reporting by James Macharia; Editing by Susan Fenton)