At a meeting with Kenyan religious leaders on Thursday, outgoing Kenya president Uhuru Kenyatta "assured them that the process of transition will be smooth", his office said in a statement.
He delivered a similar message to visiting US congressional leaders.
"Kenya will remain steadfast in entrenching the principles of good governance to ensure the country upholds its position of a shining example of democracy in the continent by maintaining peace during this transition period," his office said on Twitter.
Kenyatta had backed his erstwhile foe Raila Odinga in the August 9 poll after falling out with his deputy William Ruto, who won the presidential race by a narrow margin. Odinga has indicated he may challenge the outcome in court.
The outgoing leader has yet to publicly congratulate Ruto, who has served as deputy president since 2013 and was long considered Kenyatta's heir-apparent.
Ruto had been counting on Kenyatta's support for the top job, but in an extraordinary turn of events the president reached a pact with veteran opposition leader Odinga in 2018 that left him sidelined.
On the campaign trail, Kenyatta -- who has served two terms as head of state and could not run again -- had described Ruto as "untrustworthy".
Odinga, who at 77 was making his fifth bid for the presidency, has vowed to pursue all "constitutional and legal" avenues against a result he considers "null and void".
The outcome has also caused a schism within the Independent Electoral and Boundaries Commission (IEBC).
Four its seven commissioners have disowned the results and accused the body's head of acting outside the constitution.
Any challenge to the results must be lodged by Monday afternoon with the Supreme Court which then has 14 days to issue a ruling. If it orders an annulment, a new vote must be held within 60 days.