Zimbabwe government problems can be resolved -Zuma

* Zuma says difficult path already travelled

* Offers continued mediation to resolve disputes

* Tsvangirai says Zuma not coming as judge

* Teachers to go on strike

(adds teachers' strike, paragraphs 9-12)

By Nelson Banya

HARARE, Aug 28 (Reuters) - South African President Jacob Zuma has told Zimbabwean leaders the problems facing their fractious unity government can be overcome.

Zimbabwean President Robert Mugabe and rival Prime Minister Morgan Tsvangirai set up a coalition government in February to end a political and economic crisis, but have been feuding over implementing their agreement.

Zuma began a two-day visit to Zimbabwe on Thursday -- his first since becoming president in May -- aimed at keeping the power-sharing deal on track.

Recovery in once relatively prosperous Zimbabwe is important for South Africa given the millions of Zimbabweans driven to seek work in their much wealthier neighbour by a decade of economic decline and political crisis.

In a speech to a dinner hosted by Mugabe late on Thursday, Zuma said any outstanding disputes on the agreement brokered by his predecessor Thabo Mbeki could be resolved through mediation.

"The remaining issues are not insurmountable, and can be overcome. The most difficult path has already been travelled," Zuma said. He offered the help of the Southern African Development Community, which he currently chairs.

Mugabe and Tsvangirai's parties are wrangling over the appointment of top officials -- including the central bank governor and attorney-general -- over Western sanctions targeting Mugabe and over the pace of reform.

Zimbabwe says it needs $10 billion in foreign reconstruction aid, but has had little success in attracting it. Western countries want to see the government working effectively and implementing faster reform.

Zimbabwe's inability to secure budgetary support has seen the government coming under pressure from state employees, who currently earn an average $170 a month, boycotting work to press for higher wages.

On Friday, the Zimbabwe Teachers' Association (ZIMTA), a union whose membership exceeds 43,000, said teachers would strike on Wednesday, when the new school term is due to begin. The strike could affect public examinations, due in two months.

"Educators have, as a last resort, resolved to withdraw labour with effect from Sept. 2 until demands that salaries and allowances be adjusted progressively are met," ZIMTA president Tendai Chikowore told reporters.

ZIMTA is pressing for a wage increase to $500, from the current $165.

Although Zuma is expected to take a tougher approach to Zimbabwe than Mbeki, accused by critics of siding with Mugabe, political analysts believe he is unlikely to get the feuding parties to agree and will press them to keep talking.

"President Zuma is not coming as prosecutor or judge to the inclusive government, but will meet the principals to evaluate the progress of the agreement so far," Tsvangirai was quoted as saying by the state controlled Herald newspaper.