Meanwhile, Raila Odinga, the presidential candidate for the opposition Orange Democratic Movement, met four former African presidents who were also trying to find a diplomatic solution to the crisis in which hundreds of people have died. 'Public relations gimmickry'
Odinga, who 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.
"We have not changed our position on recognising the president. We do not recognise him," Anyang Nyongo, ODM secretary general, said on Wednesday.
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.'Broad-based' government
It also remains to be seen whether Kibaki actually plans to include Odinga's party in his "broad-based" government.
"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.
Andrew Simmons, Al Jazeera's Africa bureau chief, said that the statement from the president's office made no specific mention of Odinga.
"It simply says that there was open mind to bringing all Kenyan leaders into some sort of solution," he said.
"This, of course, succeeds the statement by President Kibaki naming 17 members of his cabinet, 17 important posts, the 17 most important posts that don't include the ODM."
The announcement of part of the cabinet also 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.Kenyans displaced
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 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.