But he is sending Condoleezza Rice, the secretary of state, to the country on Monday to back mediation by Kofi Annan, the former UN secretary-general.
Bush said: "Kenya is an issue. That's why I'm sending Secretary Rice there to help with the Kofi Annan initiative.
"The key is that the leaders hear from her first hand US desires to see that there be no violence and that there be a power-sharing agreement that will help this nation resolve its difficulties."
Bush made the remarks after holding talks with Thomas Boni Yayi, the president of Benin, in Cotonou, the country's capital.
US officials have said Washington is ready to sanction any individuals who sought to obstruct Kenyan peace moves.
Bush's African tour will highlight projects against HIV/Aids and malaria.
Earlier on Saturday, speaking in Cotonou, Bush called for a "robust" AU/UN peacekeeping force for Sudan's Darfur region, where political and ethnic conflict since 2003 has killed around 200,000 people.
He said: "No question, Sudan is a real difficult situation which we have labelled a genocide. ... We are sanctioning some, rallying others to provide aid in the hopes there will be a robust UN force in Darfur to help relieve the suffering."
He said the US was ready to "help facilitate" the movement of the peacekeeping force for Darfur.