"We urge all parties to work together to peacefully resolve any remaining concerns about the election through the existing dispute resolution mechanisms," said State Department spokesman Ned Price.
"We ask all political party leaders to continue to urge their supporters to remain peaceful and to refrain from violence during the electoral process," Price said.
Odinga narrowly lost his fifth bid for the top job to Deputy President Ruto, 55, who was proclaimed president-elect Monday on a 230,000-vote margin, less than two percentage points of the total number of ballots.
The 77-year-old veteran politician branded the result of the August 9 vote a "travesty" but stopped short of explicitly announcing that he would mount a challenge at the Supreme Court.
He also claimed he was cheated in previous losing races.
No presidential poll outcome has gone uncontested in Kenya since 2002, and the disputes have led to bloodshed in the past. Many observers do expect Odinga to mount a court challenge to the Ruto victory.
Kenya's worst electoral violence occurred after the 2007 vote, when more than 1,100 people died in bloodletting between rival tribes.