The former UN chief said President Mwai Kibaki has apologized on controversial statements he made during his address to the African Union heads of state assembly in Addis Ababa last week.
The former UN Secretary-General also expressed optimism that the Panel of Eminent African Personalities, which he is leading in talks to end the stalemate, would meet its deadline of up to 15 days.
He spoke as 300 business leaders warned him that the talks on a minimum set of agreements to end the violence had no "option to fail ".
"Everybody has agreed that what has happened should not have happened. There should be no more protests," Annan said, in an apparent reference to the burst of violence that ensued after Kibaki's statement.
Annan, who expressed distress at the exit of one of his co-chairs to the talks, South African businessman Cyril Ramaphosa, after a government delegation raised doubts that he would be biased, said progress had been made on key negotiating areas.
He said he was satisfied with the commitment of both sides to adhere to the spirit of the talks.
"There are no hardliners. Nobody has behaved in a way that makes us feel we cannot work together."
Speaking a day after Kibaki's negotiators forced Ramaphosa to step down, Annan regretted the exit of the co-mediator.
"I was bitterly disappointed that such a mediator left," he said.
Annan has emphasized the need for a co-chair to have "continuous chain" to ensure short-term issues are resolved within the seven to 15 days period.
The former UN chief, the Chair of the talks, dubbed the Kenyan National Dialogue and Reconciliation, had earlier welcomed two additional members of the negotiating teams.
He said talks on land reforms, reforming Kenya's "bloated" democratic set up and a solution to the weak constitution were in sight within days.
Kenya's Foreign Affairs Moses Wetang'ula joined the Government/PNU (Party of National Unity) team and James Orengo, a lawyer, has also joined the Orange Democratic Movement team.
The two other members of the Panel of Eminent African Personalities leading the National Dialogue, Graca Machel, wife of former South African President Nelson Mandela, and Benjamin Mkapa, the former President of Tanzania, arrived back in Nairobi on Tuesday to rejoin the talks, a statement issued by Annan's office said.
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