Kibaki And Odinga Meet
Weeks of violence followed the election results, which Mr. Odinga has rejected. After the talks, his party condemned a statement by Mr. Kibaki in which he said he was the "duly elected president".
Kenyan President Mwai Kibaki and the opposition leader, Raila Odinga, have met for the first time since last month's disputed presidential election.
The talks in Nairobi were mediated by former UN chief Kofi Annan, who said some first steps had been taken towards a peaceful solution to the crisis.
Weeks of violence followed the election results, which Mr. Odinga has rejected.
After the talks, his party condemned a statement by Mr. Kibaki in which he said he was the "duly elected president".
Meanwhile, Human Rights Watch issued a report accusing opposition officials of helping to organise ethnic violence in the Rift Valley region, in which hundreds of Mr. Kibaki's Kikuyu community were deliberately targeted and killed.
"We have evidence that Orange Democratic Movement politicians and local leaders actively fomented some post-election violence," said Human Rights Watch's acting Africa director.
ODM spokesman Salim Lone said HRW should provide concrete evidence before jeopardising mediation efforts. The party has denied previous accusations of ethnic cleansing.
The unrest triggered by the election on 27 December has left more than 650 people dead and driven 250,000 from their homes.
The breakthrough meeting, which last about one-and-a-half hours, was hosted by Mr. Annan at the president's office at Harambee House in central Nairobi.
Afterwards, the former UN secretary general emerged to say progress had been made during the meeting, describing it as "a very encouraging development".
He was followed by Mr. Odinga and Mr. Kibaki, who both made statements in front of dozens of cameramen and journalists outside, and a few hundred people who had gathered in the street opposite.
Both men shook hands with broad smiles and expressed their commitment to peace and asked their supporters to maintain calm as they continued the newly established dialogue.
"We have taken the first vital steps in resolving electoral disputes," Mr. Odinga said.
"I pledge to all Kenyans that my team and I will spare no effort to resolve this crisis," he added. "We are ready to walk the extra mile if that will enable Kenyans to get peace."
Mr. Kibaki also welcomed the talks and insisted he was committed to dialogue.
"As government, we are determined to get to the underlying causes of these unprecedented events and to lead the nation in a process of healing, reconciliation and lasting harmony," he said after Mr. Odinga's statement.
Differences between the two remained, however, with Mr. Odinga insisting on a sustainable peace being dependent on justice and Mr. Kibaki stating he had been "sworn in as your duly elected president of Kenya".
Mr. Kibaki's comment was later criticised by the opposition, who said it showed he had "no intention whatsoever of embarking on this journey with the people of Kenya".
"We denounce and categorically reject the unfortunate statement from Mr. Mwai Kibaki that he is the duly elected president of Kenya and that the current crisis can be resolved internally," ODM Secretary General Anyang N'yongo said.
The BBC's Adam Mynott in Nairobi says the symbolism and significance of this meeting was enormous, but there is still a great deal of work to be done and compromise required for them to resolve their differences and reach an agreed way forward.
Detailed talks between the rivals are due to begin in the morning.
The announcement of the talks came as a surprise to many in Nairobi. Several earlier attempts to get the rivals to meet had failed, with Mr. Kibaki insisting on direct talks and Mr. Odinga refusing to meet without a mediator.
On Wednesday, Mr. Odinga called off a mass protest planned for Thursday in Nairobi after holding talks with Mr. Annan.
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