Odinga is behind in preliminary counts against Deputy Prime Minister Uhuru Kenyatta, accused of crimes against humanity during the 2007 violence.
Kenya's election commission said Wednesday it was forced to hand-count ballots after technical failures. It had reported ballot complications at some voting locations this week.
Charles Kanjama, a lawyer who worked on election disputes, said less than half of the votes have been counted. Despite some anxiety, he said, there's been nothing to indicate a less-than-fair vote, reports Bloomberg News.
U.S. State Department spokesman Patrick Ventrell said despite reports violence, the vote was seen largely as a peaceful event.
"We urge that any election disputes be resolved peacefully through the Kenyan legal system," he said in a statement. "It is critical that Kenya avoid the post-election violence that marred the December 2007 presidential contest."
His sentiments were echoed by U.N. Secretary-General Ban Ki-moon who said he was encouraged by the election so far but mindful of the 2007 conflict.
"A peaceful, credible conclusion to the election is within Kenya's reach and would be a significant step for Kenyan democracy and stability," Ban said in a statement.