(Releads with Mbeki comments)

By Cris Chinaka

HARARE, Jan 17 (Reuters) - South African President Thabo Mbeki said on Thursday he was optimistic about the chances of ending Zimbabwe's political crisis after holding separate talks with President Robert Mugabe and the opposition.

But he offered no evidence of a breakthrough.

"I don't doubt the commitment of the Zimbabwe leadership to ensuring that all the country's problems are solved," he told reporters. "It's really work in progress and very good progress."

Mbeki met Mugabe amid signs the government would not yield to opposition demands for a new constitution. He then held talks with officials of the two factions of the opposition Movement for Democratic Change (MDC).

Mbeki has been mediating between Mugabe's government and the MDC for nearly a year at the urging of countries in the Southern African Development Community (SADC) grouping.

South Africa's opposition and Western diplomats accuse Mbeki of being too soft on Mugabe. He and other SADC leaders say pressuring Mugabe would only fuel political tensions in Zimbabwe and undermine efforts to tackle an economic meltdown.

Irish Prime Minister Bertie Ahern said this week after meeting Mbeki in Pretoria a breakthrough in the negotiations might be achieved soon and an agreement that would pave the way for free elections in March in Zimbabwe was only days away.

Asked if an agreement between the MDC and Mugabe's ZANU-PF was possible before March elections, Mbeki was guarded.

ELECTION CHALLENGE

"I think everybody is very conscious that elections are coming in March, but everybody is also conscious of the task that has to be handled before then," he said.

Zimbabwe's government-controlled Herald newspaper said on Thursday there was a serious division between ZANU-PF and the MDC over the adoption of a new constitution.

The Herald said the MDC wanted a new constitution to be adopted before presidential and parliamentary polls were held, or the polls postponed. Government negotiators believed the MDC was making its demands under directives from London, it said.

Mugabe, in power since independence from Britain in 1980, accuses the MDC of being a puppet of the former colonial power, Britain, which is denied by the opposition party.

The Zimbabwean leader has vowed to run for another five-year term, despite accusations that his government has abused human rights, rigged previous elections and destroyed the economy.

Mugabe's Western foes see him as a ruthless dictator whose people are victims of his mismanagement of what had been southern Africa's breadbasket.

But southern African leaders look up to him as a liberation hero who stands up to the United States and Britain, even though he is accused of bringing Zimbabwe to its knees in the process.

Zimbabweans are battered by inflation of more than 8,000 percent and chronic shortages of food and fuel. Thousands cross illegally into South Africa every day to look for food and work.

Political analyst and Mugabe critic John Makumbe said the opposition would be making a mistake by participating in elections before a new constitution was put in place.

"The master of deception, ZANU-PF, is leading the MDC up the garden path," Makumbe said. "It stands to reason that all the MDC and ZANU-PF have agreed upon through the mediation talks is little more than efforts to hoodwink SADC." (Additional reporting by Paul Simao in Johannesburg; Editing by Michael Georgy and Elizabeth Piper)

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