Annan, who is leading a panel of African leaders, is urging the two to open talks and end a crisis that has hundreds of Kenyans dead and displaced a quarter of a million.
Police had banned Thursday rallies following clashes at demonstrations last week that killed 80 people, bringing the overall death toll since the election to more than 650.
Yoweri Museveni, the Ugandan president who was among the first leaders to recognise Kibaki's legitimacy after the contested poll, met Kibaki on Wednesday.
Several international attempts to bring the two sides into face-to-face talks have so far failed.
Riot police and protesters on Wednesday fought running battles at a funeral procession held by the opposition for Nairobi slum residents killed in violence over the country's disputed election.
Odinga, leader of the Orange Democratic Movement (ODM), fled the scene after the latest clashes in Nairobi, the Kenyan capital.
He said in a statement: "This government first committed the unforgivable crime of stealing the vote, it then kills those who protest, and finally, when people come to mourn the departed, it assaults them as well.
"This latest attack on a peaceful gathering shows that this government is running amok ... To assault peacefully gathered mourners is a terrible crime, made much worse when the peoples' leaders, including the winner of the presidential election, are the targets."
At least 12 people were killed in Kenya overnight amid fighting between rival tribes and gangs, police said on Thursday.
"Six were hacked to death in Kaptembwa and two others in Bahati," two settlements near the town of Nakuru, northwest of Nairobi, a police commander said.
Police shot dead two men in the central town of Limuru when members of president Mwai Kibaki's Kikuyu tribe started evicting residents from rival tribes from their homes, a police commander said.
In the Nairobi slum of Kariobangi, a man was hacked to death in fighting between rival tribal gangs.