"I am ready to have dialogue with the concerned parties once the nation is calm," Kibaki said, striking a more conciliatory note than his supporters' recent rhetoric.
A week of bloodshed since a December 27 election has killed more than 300 people and threatens to wreck Kenya's reputation as one of Africa's most promising democracies and strongest economies.
"I am deeply disturbed by the senseless violence instigated by some leaders," Kibaki told reporters on the lawn of his residence. "Those who continue to violate the law will face its full force."U.S. President George W. Bush urged Kenyans to refrain from further violence and called on Kibaki and opposition leader Ralia Odinga to "come together" to resolve the dispute.
"It's very important for the people of Kenya to not resort to violence," Bush told Reuters in an interview on Thursday.
Asked whether Kibaki and Odinga should share power, Bush said, "I believe that they have an opportunity to come together in some kind of arrangement that will help heal the wounds of a closely divided election."
The European Union urged them to form a coalition government.
Currency and stock trading was halted in Nairobi on Thursday, with the shilling and share prices both down about five percent since the troubles began.
The disputed polls have unleashed vicious tribalism around Kenya and both sides accuse the other of ethnic cleansing.
"This is genocide being conducted by the political class illegally sitting in State House," Odinga said after taking journalists to view corpses with gunshots at a city mortuary.
He named two key Kibaki allies as backing a Kikuyu gang behind some of the killings. On Wednesday the government accused Odinga's Orange Democratic Movement (ODM) of organised genocide.
After police clashed for hours in Nairobi with thousands of protesters angered by Kibaki's victory, the opposition called off a planned rally in the city's Uhuru (Freedom) Park, saying it wanted to save lives.
The opposition vowed to try again on Friday.
"The rally is on for tomorrow," spokesman Salim Lone said.
Shots cracked out as police fired over the heads of protesters on Thursday morning and fires raged in the slums.
Flames burst from a large crucifix suspended from the roof of a burning church in Kibera, one of Africa's largest slums, and a hotbed of support for Odinga.
Reuters reporters saw at least four bodies lying in the dust near the Mathare slum. Three were beaten and slashed to death by mobs and the fourth killed by a falling power cable.
