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By Andrew Cawthorne and C. Bryson Hull

NAIROBI, Feb 8 (Reuters) - Kenya's feuding political parties may reach a breakthrough within days to help end violence after a disputed election that has left more than 1,000 people dead, mediator Kofi Annan said on Friday.

The former U.N. chief's upbeat assessment came as local media speculated a power-sharing deal was on the cards between President Mwai Kibaki and opposition leader Raila Odinga, whose disagreement has brought unrest shattering Kenya's stability.

"I sincerely hope that we will conclude our work on item three, the settlement of the political issues, by early next week," said Annan, who is mediating the dispute.

"We are all agreed a political settlement is necessary with a little patience and a bit of luck."

In addition to the killings, the ethnic attacks and battles between police and protesters have uprooted more than 300,000 people, wrecking Kenya's image as a stable business, tourism and transport hub.

Negotiators for Kibaki and Odinga have agreed on principles to stem violence and help refugees, but were stuck this week on the crucial dispute over the vote tally.

Odinga's Orange Democratic Movement (ODM) says Kibaki supporters rigged the vote, but Kibaki's Party of National Unity (PNU) says the opposition cheated in its heartland and points to the election board's announcement Kibaki had won.

Annan has given both sides until mid-February to resolve that issue and then move on to tackle deeper, underlying problems like land and wealth inequality within a year.

On Friday, Kibaki and Odinga met for the third time since the crisis began. Their negotiators, meanwhile, shook hands warmly with each other after another day's talks in the warmest body-language seen yet between the two sides.

BOWS AND ARROWS

Annan would not be drawn on details of their progress. "Please don't pay much attention to the speculation," he said.

And unusually, officials on both sides of the political divide also declined to give details of the progress in negotiations, though they confirmed talks were moving forward.

"There is positive news, but no final solution yet," an opposition leader, William Ruto, told Reuters.

Kenya's election unrest has laid bare deep divisions over land, wealth and power that date from British colonial rule and have since been stoked by politicians.

But violence has dropped sharply this week.

"We cannot afford our people using bows and arrows, people being pulled out of buses to be asked 'which language do you speak?' and then being chopped," said government negotiator Mutula Kilonzo, stressing the urgency of successful talks.

The latest international dignitary to fly into Kenya was U.N. humanitarian boss John Holmes, on a three-day trip to see for himself the damage and suffering around the nation. He was due to visit the worst-hit Rift Valley area on Saturday.

Foreign ministers from the regional IGAD bloc threw their weight behind Annan on Friday, rejecting opposition charges they were visiting Kenya to launch separate talks to undermine him. (For special coverage from Reuters on Kenya's crisis see: http ://africa.reuters.com/elections/kenya/) (Additional reporting by Duncan Miriri, George Obulutsa; Editing by Caroline Drees)

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