However, the Kenyan government told Al Jazeera that Kufour was not there to mediate but was on a fact-finding mission.
"I think President Kufour, in announcing he was coming here, he didn't use the words that he was coming here to mediate," Martha Karua, the justice minister, said.
"That's a creation of the press and I don't know whose agenda it is in the international community ... the dispute will be resolved in court."
Kibaki named Stephen Kalonzo Musyoka, the leader of the ODM Kenya party, as his vice-president as well announcing several key allies were to be handed cabinet posts.
ODM Kenya, a separate party to Odinga's Orange Democratic Movement, came a distant third in recent elections.'Gimmick'
"The whole thing is a gimmick, the cabinet is a joke," Anyang Nyongo, secretary-general for Odinga's ODM, said.
"We do not recognise the president and therefore we won't recognise his cabinet."
Odinga had earlier agreed to meet Kibaki, following pressure from Jendayi Frazer, Washington's most senior diplomat for African affairs.
The announcement also sparked demonstrations 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 at the entrance to slums surrounding the city, lit bonfires and carried placards asking why the president named the cabinet.
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.'Desperate situation'
"The situation is indeed getting desperate and 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," a British diplomat told the AFP news agency.
But Kufour is not the only potential mediator in the country attempting to prevent the crisis from deepening.
Frazer has been asked to prolong her mission and four former African presidents - Tanzania's Benjamin Mkapa, Mozambique's Joachim Chissano, Botswana's Katumile Masire and Zambia's Kenneth Kaunda - are also in the country.
The United States is a key Kenyan donor and George Bush, the US president, has urged the government and opposition to hold "good faith" talks and end the violence.