By Marius Bosch

JOHANNESBURG, Jan 9 (Reuters) - The world should not give up hope of a peaceful solution to Kenya's crisis as the country's president and rival opposition leader are open to negotiations, Nobel peace laureate Desmond Tutu said on Wednesday.

"I don't think we should be too despondent," said Tutu, a former Archbishop of South Africa who shuttled between the rival camps of President Mwai Kibaki and opposition leader Raila Odinga on a mediation mission last week.

"The situation is like a kind of a rollercoaster. Sometimes you get to be on a high because it looks as if things are promising and then you plumb the depths because something has happened or somebody said something," he said.

Tutu said in his meetings with Kibabi and Odinga, both men had shown themselves to be open to talks.

"My impression was that they were genuinely open to the possibilities. When I met with the president, he wasn't too keen to speak about a government of national unity but didn't mind speaking about a coalition," Tutu said in a telephone interview from Cape Town.

Post-election turmoil in Kenya has killed about 500 people and left about a quarter of a million people displaced in the east African nation seen only months ago as a bright hope for democracy.

The two rival Kenyan leaders have not met face-to-face since trouble started when Kibaki was sworn in on Dec. 30, despite huge international pressure.

On Wednesday, African Union chief John Kufuor met Kibaki and Odinga separately to try to defuse the crisis which has damaged Kenya's reputation for stability and hurt the key economic sectors of tea and tourism.

Washington says the vote count was "obviously flawed" while London calls it "plagued by irregularity", and Tutu said claims by Odinga's Orange Democratic Movement (ODM) to have won the Dec. 27 presidential vote had some substance.

"Mr. Kibaki's party lost a few of its cabinet ministers which seems to indicate that the claims by the ODM to have won the presidential elections have some very considerable substance to support them," he said.

Officials say 486 people have died in election-related violence. Aid workers put the figure at more than 500 and the opposition say nearer 1,000 people died in clashes between police and protesters, ethnic fighting, and looting.

Tutu said Kenyan church leaders had indicated that the tensions had been building over several years with many Kenyans feeling marginalised and angry at the concentration of wealth and power in the hands of a small group.

"The underdogs remained underdogs and there was still little prospect of their status changing. The resentments were building up over years." (Editing by Jon Boyle)

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