A powerful South African labour leader threatened on Sunday to withdraw support for President Jacob Zuma's African National Congress, ending a long- standing alliance strained by a nearly three-week-old strike.

Adding to the pressure, a union representing tyre makers announced a strike for higher wages from Monday. Thousands of armed forces unionised members are also thinking of striking.

This month's strike by about 1.3 million state workers has presented Zuma with one of his most serious challenges since taking office more than a year ago, with unions trying to link the labour action to Zuma's political future.

We will not make a mistake again of voting into power our worst political butchers, COSATU Secretary-General Zwelinzima Vavi said at a rally.

COSATU helped Zuma win the presidency and its support is essential if he wants to seek re-election. Vavi last week said the alliance with the ANC forged in the struggle to end apartheid was on the verge of rupture.

COSATU has already threatened to widen the state workers' strike later this week to all of its member unions who it says represent about 2 million workers.

A one-day strike set for Thursday will probably not do much economic damage but COSATU has said the action could turn into an indefinite strike, which would cause major damage in industries including mining, which alone is responsible for about 5 to 6 percent of GDP.

Analysts expect Zuma and the ANC government, which has typically given in to labour's demands, to reach a deal soon, tilted in favour of the unions, and worry later about the damage to state spending.

Zuma also does not want to have the dispute hanging over him heading into an ANC policy-setting meeting in late September.

It wouldn't surprise me if there was some sort of resolution by the end of the week, labour analyst Tony Healy told Talk Radio 702.

Zuma on Saturday accused striking state workers of abandoning the sick at hospitals and said he expected a deal to be reached soon to end the labour action.

An expanded strike would add to worries about prospects for growth after the economy slowed more than expected in the second quarter of 2010 as mining contracted and manufacturing expanded at a slower pace.

The government has said it cannot afford the state workers' demand of an 8.6 percent wage rise, more than double the inflation rate, and 1,000 rand ($135.8) a month as a housing allowance. It has offered 7 percent and 700 rand.

Any agreement to end the dispute is likely to swell state spending by about 1 to 2 percent, forcing the government to find new funds just as it tries to bring down a deficit totalling 6.7 percent of gross domestic product.

Bond, stock and rand trading have mostly been unaffected by the strike but market players said that could change if there is no deal by the end of the week and if the strike widens to industries which could hurt local shares and dent sentiment.

(Editing by Charles Dick)