Kufuor was supposed to meet the two men together but that fell through, leaving him to shuttle between them in separate meetings that officials say made little headway.
Kibaki reportedly told Kufuor that he had initiated dialogue with opposition leaders and his office said "now that peace was returning ... his partially formed government would continue to reach out to Kenyan leaders".
But Kufuor's mission was made that much harder Kibaki's act of naming a partial cabinet without any members of Odinga's main opposition group just hours before his arrival on Tuesday evening.
Analysts say Kibaki made the appointments ahead of the mediation process to cement his claim to the presidency.
Andrew Simmons, Al Jazeera's Africa bureau chief, said that the statement from the president's office made no specific mention of Odinga, simply saying there was an openness to bringing all Kenyan leaders into some sort of solution.
The appointments sparked a violent response from opposition supporters - after three days of relative calm - already angry at what they believe was a rigged election.
The US, which had expressed disappointment over the cabinet announcement, said on Wednesday that it was satisfied with Kibaki's clarification that the appointments were meant to keep the government running, not antagonise the opposition.
"Absolutely we were disappointed. He's now come out and clarified where he stands on this, and that's very positive," Sean McCormack, the state department spokesman, said.
'Public relations gimmickry'
An opposition spokesman said Odinga discussed forming a transitional government, a vote recount and an entirely new vote as possible options to end a crisis that has dented Kenya's reputation for stability in volatile east Africa.
Odinga, whose Orange Democratic Movement (ODM) accuses Kibaki's government of rigging the presidential election 11 days ago, dismissed Tuesday's cabinet announcement as "public relations gimmickry".
He said that Kibaki was "trying to deflect attention from and undermine" international mediation and refused to meet the president without Kufuor being present.
Anyang Nyongo, ODM's secretary-general, said on Wednesday that the party had "not changed our position on recognising the president. We do not recognise him".
Odinga had earlier agreed to meet Kibaki, following pressure from Jendayi Frazer, Washington's most senior diplomat for African affairs.
Kibaki named Stephen Kalonzo Musyoka, the leader of the ODM Kenya party, as his vice-president as well announcing that several key allies were to be handed cabinet posts.
ODM Kenya, a separate party to Odinga's ODM, came a distant third in the recent elections.
A British diplomat said the situation was "indeed getting desperate".
"It's up to Kufuor to defuse it now. How he will do it is unclear because, by naming the cabinet, the government told him, 'thanks for coming, but no mediation please'," the diplomat said.
The announcement of the partial cabinet sparked renewed violence overnight in the western city of Kisumu.
A police commander said that officers fired into the air to disperse up to 300 protesters who had blocked a road, lit bonfires and carried placards asking why the president named the cabinet.
Hundreds of ethnic Kamba fled the city for Nairobi after it was announced that Musyoka, a member of their ethnic group, would be vice-president.
Thousands of Kibaki's Kikuyu people have left their homes in Kisumu in a week of riots and ethnic clashes that saw buildings burnt to the ground and more than 500 people killed across the country.
The UN says 250,000 Kenyans have been displaced by post-election violence, and aid groups have warned of a potential health emergency in makeshift camps in schools, hospitals and churches in the Rift Valley region of western Kenya, as well as Nairobi's slums.
The UN has diverted 24 tonnes of blankets and soap intended for refugees from Somalia to help displaced Kenyans.
Emmanuel Nyabera, spokesman for the United Nations High Commissioner for Refugees, said that the agency would start distributing the aid to families in various parts of Nairobi, where riots and political killings, mostly in the slums, have left many homeless.
"Considering that Kenya has played host to refugees for years and years, we thought it our obligation to also intervene in the Kenya humanitarian situation," he said.