* Mineworkers say Eskom power utility workers may strike
* Telkom workers to continue strike next week
(Adds context, background)
By James Macharia
JOHANNESBURG, Aug 4 (Reuters) - South Africa's biggest union on Tuesday threatened strikes at state power utility Eskom from next week and said it would shut down electricity across the country to press wage demands.
Power failures early last year temporarily crippled output from mines in the world's top platinum producer, also a top gold miner.
As well as disrupting Africa's biggest economy, a power strike would be a further challenge to new President Jacob Zuma's authority as he tries to lead South Africa through its first recession in 17 years and defuse anger in poor townships.
The National Union of Mineworkers has the biggest number of workers represented by any union at Eskom with about 16,000 members. It said its members had agreed to take part in mass action across the country starting next Monday, culminating in a complete stayaway.
"There will be a complete shutdown of power across the country," NUM spokesman, Lesiba Seshoka said.
Workers at South African telephone group Telkom also said they would continue a strike into next week after unions walked away from talks to end the latest in a round of damaging industrial disputes.
Employees at Telkom, Africa's biggest fixed-line operator, began a two-day strike on Monday after a month of sometimes violent protests that saw tens of thousands of council workers downing tools and taking to the streets.
UNIONS FLEX MUSCLE
The council workers and others came to terms last week, but the protests have led to pay deals of nearly double inflation that economists say may trouble an economy now in recession.
Unions that helped bring Zuma to power in April elections are flexing their muscles, seeking payback for their support. But Zuma, who portrays himself as a champion of the poor, is constrained by the recession.
Foreign investors who worry Zuma may give in to labour and steer the economy to the left have not been alarmed by strikes so far. But they could take serious notice if mineworkers strike and shut down power.
The Communications Workers Union (CWU), representing 44,000 employees, said more than 9,000 Telkom workers would return to work on Wednesday but resume industrial action on Friday and Tuesday of next week.
In a statement Telkom said about 1,600 took part in the strike, and that it was committed to reducing wage disparities while also ensuring the sustainability of the company and job security.
The group said it was investigating acts of vandalism and sabotage carried out during the strike.
The CWU is demanding that Telkom first move employees to higher pay scales before implementing a 7.5 percent wage increase.
Besides job boycotts, pressure on the government has also come from poor township residents, who have demonstrated to back their demands for better living conditions for millions of blacks who still lack adequate housing, electricity and water 15 years after the end of apartheid. (Additional reporting by Alison Raymond; Writing by Michael Georgy)