In a statement on Wednesday, the Rev Dr Samuel Kobia, a Kenyan, called on Kibaki and his opponent Raila Odinga to "put the interests of the nation and the surrounding region above other concerns".
Kobia also urged churches in Kenya to "do their part in pursuing the common good of their communities and country" by fulfilling their role "in ensuring respect for human life and seeking reconciliation between neighbours".
This is something "especially urgent amid ominous signs of ethnically targeted hatred and violence", he added.
Vigilante mobs brandishing crude weapons have wrought havoc in parts of Kenya, burning shops and houses, in days of violence that is threatening to destabilise the whole eastern African region.
Cries rang out from around the international community on Wednesday for calm to be restored to the country as Nobel peace laureate Archbishop Desmond Tutu flew into Nairobi in a bid to stem the bloodshed.
The former Archbishop of Cape Town and lifelong peace activist landed in Nairobi on Wednesday with offers to help in the mediation between President Kibaki and Odinga, who accuses the President of rigging his re-election last Sunday.
Kenyan election commission head Samuel Kivuitu pronounced President Kibaki the winner of Sunday's election.
He told reporters, "Even Desmond Tutu called me from South Africa and said he wants to meet me."
Ghanaian president and African Union chairman John Kufuor spent much of Wednesday in key meetings to help mediate in the crisis, as the death toll climbed to 300.
Prime Minister Gordon Brown had appealed on Tuesday to Kufuor and former Sierra Leonean President Ahmad Tejan Kabbah, the head of the Commonwealth's electoral observer mission, to intervene in Kenya.
He backed Kufuor's decision to visit Kenya in person.
"I have just talked to President Kufuor of Ghana ... I welcome his decision, that he will announce later today, that he will go to Kenya. He will meet President Kibaki and Mr Odinga tomorrow," Brown said in a statement.
He added, "He will call on them to urge their supporters to end violence and he will work with the parties to ensure that reconciliation is brought about and perhaps a chance that some of the people who are at the moment opponents may join a government of national unity."
Chris Melville, senior Africa analyst at Control Risks consultancy in London, said, "Kufuor is one of the most credible and consistent champions of the more progressive aspects of African Union politics ... for that reason he should be able to bring some pressure to bear on Kibaki and Odinga."
Foreign Secretary David Miliband and US Secretary of State Condoleezza Rice urged restraint and intense political dialogue in a joint statement issued on Wednesday, as France, Germany and Japan added to international appeals for calm.
Analysts are skeptical, however, that the appeals from Western powers will be enough to put a stop to the violence.
"Pressure from outside powers - for example in reducing aid - is unlikely to bring about an immediate halt to violence. It seems there is little the international community can do at this stage," said Razia Khan, Africa economist for Standard Chartered Bank.
