By Duncan Miriri

NAIROBI, Feb 28 (Reuters) - Mediator Kofi Annan launched a new bid on Thursday for a political compromise to end Kenya's post-election crisis, bringing the country's feuding leaders to the same table for the first time in a month.

Annan and many Kenyans want President Mwai Kibaki and opposition leader Raila Odinga to make tough decisions that will lead to a power-sharing agreement after talks between negotiators for the two men hit a deadlock on Tuesday.

African Union Chairman and Tanzanian President Jakakya Kikwete also attended the talks, extending his stay in Kenyan capital Nairobi by a day in hope of pushing through a deal.

Odinga and Kibaki have come under intense pressure to compromise over Kibaki's disputed re-election in a Dec. 27 vote, which sparked ethnic violence that killed 1,000 people and displaced 300,000 more.

The opposition had threatened to hold mass street protests on Thursday, but called them off after meeting Annan, a former U.N. Secretary-General, on Wednesday.

Kibaki has agreed to create a prime minister post, as demanded by the opposition, but the two sides are still far apart on how that would be done, what powers a premier would have and how many cabinet jobs Odinga's side will get.

Annan said on Wednesday he believed the two sides could strike a deal.

"Issues that divide the parties are bridgeable ... with political will," Annan told reporters. "The solution must be found in the mediation room."

The crisis that exploded after Kibaki was sworn in on Dec. 30, amid Odinga's claims the election was rigged, seriously hurt Kenya's reputation as a stable, prosperous nation in a turbulent corner of Africa.

The stalled negotiations also prompted criticism from the United States and European Union, in the latest diplomatic pressure to force a rapid resolution of the crisis. (Additional reporting by Wangui Kanina and Bryson Hull; Writing by Giles Elgood; editing by Bryson Hull) (For in depth coverage on Reuters Africa Web site: http://africa.reuters.com/elections/kenya/ )

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