Outgoing President Mwai Kibaki met Tuesday with Deputy Prime Minister Uhuru Kenyatta and his running mate William Ruto to congratulate them on winning last week's election, The Daily Nation newspaper in Kenya reports.
Kenyatta scored a narrow victory over Prime Minister Raila Odinga, although Odinga said he'd challenge the results in courts.
Post-election violence in 2007 in Kenya left thousands of people dead. Last week's election was the first under new laws meant to prevent a repeat of the 2007 violence.
Ban, in a statement issued through his spokesman's office, reminded Odinga and Kenyatta "of the commitments they have made throughout this process to channel any electoral grievances through the established legal avenues."
Kenyatta in July faces the International Criminal Court on charges of committing crimes against humanity during the violence in 2007.
U.N. spokesman Martin Nesirky said the world body would maintain only essential contacts with Kenyatta if he were indicted by the ICC. Normal relations would be maintained for now provided Kenyatta cooperates with the court, the Kenyan report notes.