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.
