But they agreed that International Criminal Court Chief Prosecutor Luis Moreno-Ocampo should write to them requesting a meeting in the coming week.
The fate of post-election violence masterminds appears to have been sealed during the three-man meeting at the Presidents Harambee House office when the President and PM told Mr Annan that Kenya was unlikely to set up a local tribunal.
The meeting was closed even to their aides, but Cabinet ministers who were later briefed about the talks said that Mr Annan would ask Mr Moreno-Ocampo to write to the two leaders asking for a meeting to discuss the next step after Kenya failed to set up the tribunal.
The meeting could be held as early as next week, the ministers, who cannot be named discussing the proceedings of the top-level meeting, said.
Parliament has twice refused to pass laws to establish the tribunal with MPs saying the suspects should be tried at The Hague.
A statement issued by the two leaders after the hour-long meeting on Monday showed that they had given up on locally trying the ministers, MPs and business people accused by the Waki Commission of planning and financing the chaos in which 1,133 people were killed and over 650,000 displaced from their homes.
Even though the government preferred reconciliation, President Kibaki and Mr Odinga left the door open for suspects bearing the greatest responsibility over the post-election violence to be tried by the International Criminal Court.
On Tuesday, Mr Annan had a dizzying round of meetings, including sessions with MPs from the Official Opposition Caucus, the Kenya National Commission for Human Rights representatives, religious leaders, the Interim Independent Electoral Commission, the Interim Independent Boundaries Commission, EU representatives, African Union envoys and the Kenya Private Sector Alliance.
Mr Annan also met Vice-President Kalonzo Musyoka.
He urged the electoral commission to devise a system that would shield Kenya from further poll violence.
Interviews with those who have met Mr Annan show that Mr Annan acknowledges that progress has been made on reforms and was surprised that the government has been so poor in communicating its achievements.
They also said Mr Annan was impressed by the technical teams in the various commissions whose members he was convinced were able to execute their mandate.
But he was also worried about the political obstacles to reform and the danger of politicians interfering with the work of the technical teams.
He gave the example of attempts by PNU and ODM to influence the work of the Committee of Experts on the Constitution and recruitment of key personnel at the interim electoral commission.
Those who spoke to him said his main focus seemed to be that a new constitution be in place before the next election. Though he spoke about the three-tier justice idea with the Hague prosecuding the masterminds, a local tribunal dealing with smaller offenders and the Truth, Justice and Reconcilliation Commission dealing with long term injustices he appeared convinced that justice was best dispensed locally.
He also appeared keen on an example being made of those who formented the violence to prevent a recurrence.
Ministers privy to the talks told the Nation that they had formed the impression Mr Annans visit aimed to prepare the ground for Mr Moreno-Ocampo or an official from his office later this month to start the process of investigating the atrocities in Kenya.
The ministers said it was their understanding that Mr Annan asked the President and the PM whether there remained any possibility of establishing a tribunal.
The two, in reply, said Parliament had opposed the idea and they would not be averse to the intervention of The Hague.
But when asked whether they would be willing to write to Mr Moreno-Ocampo inviting him to step in, they declined to do so, only agreeing that Mr Annan should inform the prosecutor to write to the President and the PM asking for a meeting.
Mr Annan will address a press conference at the Serena Hotel this afternoon before leaving the country.
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