Raila Odinga, the leader of Kenya's opposition Orange Democratic Movement, accuses President Mwai Kibaki of rigging his re-election last Sunday in a dispute that has set off latent tribal tensions in the country, and resulted in days of killing and riots.
The worst of the violence came on Tuesday when a church in Eldoret was torched by a mob of protesters, killing around 30 people.
The former Archbishop of Cape Town and lifelong peace activist flew into Kenya on Wednesday to help in the mediation efforts and spent part of Thursday in talks with Odinga.
"I appeal to both leaders to meet and talk about points of disagreement," said Tutu on his arrival in Nairobi from South Africa.
President Kibaki appealed on Thursday for the violence to come to an end, saying that he was prepared to enter talks with the opposition as soon as calm had returned to the country.
"I am ready to have dialogue with the concerned parties once the nation is calm and the political temperatures are lowered enough for constructive and productive engagement," Kibaki told reporters on the lawn of his State House residence in Nairobi.
