President Mwai Kibaki and opposition leader Raila Odinga shook hands and smiled after the closed-door talks, brokered by former U.N. boss Kofi Annan.

"I think we began to take some fair steps towards a peaceful solution," Annan told reporters gathered outside Kibaki's central Nairobi office, where the discussions took place.

The two leaders had not talked since the December 27 polls despite intense pressure from Western powers and millions of anxious Kenyans horrified by their country's slide into chaos.

Odinga, who says Kibaki stole the election, said talks would continue until a solution was found.

"I pledge to all Kenyans that my team and I will spare no effort to resolve this crisis," he said.

Kibaki vowed to personally lead the east African country to unity and peace.

"I appeal to all Kenyans to remain calm and to shun violence as we endeavour to find solutions," he said. "I am confident that together, our experience, unity and determination will make it possible for us to overcome the challenges."

When the pair shook hands, hundreds of onlookers cheered.

Odinga and other officials from his opposition Orange Democratic Movement (ODM) agreed after meeting Annan on Wednesday to call off protests planned for Thursday.

The opposition demanded an outside mediator to solve a crisis that has split Kenya down tribal and political lines, after Kibaki narrowly won the closest election in the east African nation's history in a vote rife with rigging.

Odinga says Kibaki stole the election.

Hundreds have died and 250,000 been forced to flee their homes in a combination of politically incited ethnic killings and police action to quell protests that frequently degenerated into rioting and looting.

In Odinga's western stronghold of Kisumu on Thursday, some youths burned tyres, saying they were angry their leader had been caught in police teargas on Wednesday at a memorial service for some of the dead. Local media said two people were killed in the flashpoint Rift valley town of Molo.

ETHNIC KILLINGS

On Thursday, Human Rights Watch (HRW) said it had "evidence that ODM politicians and local leaders actively fomented some post-election violence", in the Rift Valley.

"Opposition leaders are right to challenge Kenya's rigged presidential poll, but they can't use it as an excuse for targeting ethnic groups," HRW's Georgette Gagnon said.

The Rift has seen some of the worst violence in the crisis, including the burning to death of 30 members of Kibaki's Kikuyu ethnic group in a church by members of the Kalenjin tribe.

HRW said at least 400 had been killed in ethnic clashes there, and that ODM mobilisers and local elders urged Kalenjins "to contribute money toward the purchase of automatic weapons".

It quoted Kalenjin sources who said plans were still in place to attack camps of displaced Kikuyus and so far unaffected areas. It urged police to step up protection.

The violence has shattered Kenya's image as a stable, democratic country with the region's strongest economy. Its core tourism industry has seen mass cancellations and the shilling currency hit an 18-month low on Wednesday before recovering.