Tuesday's election pitted incumbent President Uhuru Kenyatta, who is seeking his final five-year term in office, against Raila Odinga, a veteran opposition leader who is vying for power for the fourth time.
"I'm myself willing to accept the will of the people, so let them too", he told reporters gathered outside a polling station in the small town of Gatundu outside Nairobi, where he cast his vote.
Videos circulated on social media of skirmishes and tear gas allegedly being used in some parts of the country earlier Tuesday, but CNN did not witness any violence.
Kiingati, who wore a wool cap and walked with a cane to the ballot box, smiled broadly when an election official marked her finger with indelible ink after she voted.
If he loses, he'll be the only president in the country's history to not win re-election.
Former US president Barack Obama, whose father was born in Kenya, led a chorus of worldwide calls on the eve of the vote for a peaceful election.
That prompted sharp criticism from Odinga, who also ran against Kenyatta in the 2013 vote and unsuccessfully challenged the results in court with allegations of vote-tampering.
"We have our projections from our agents which show we are ahead by far", he added. Kenyan radio said one person was killed in clashes in the southern Kilifi area.
"Today is a very important day for Kenyans". Kenya has 44 official tribes and decision hopefuls ordinarily shape cooperations with lawmakers from other ethnic gatherings to widen their allure. Officially, election authorities have up to a week to declare the outcome. Results are then sent to a national tallying center in Nairobi.
People are voting in Kenya's general election amid fears that the result could trigger communal violence.
Reaction to the result could partly depend on the performance of Kenya's electoral commission, which will collect and count the ballots in the coming days. Shortly after she arrived, she went into labour, and, with the assistance of bystanders, gave birth to a baby girl while still at the polling station.
At some polling stations, the queues were still there when polls closed 12 hours later. "None of these incidents have affected the process of voting".
Kenya's election has been dogged by fears of another outbreak of violence similar to the one seen after Mr Odinga's election loss in 2007.
In a bid to ease tensions Kenyatta addressed the nation Monday night, urging citizens to vote "in peace".
"There are attempts to manipulate the results", Odinga said.
After a trip to a local health clinic, she returned and cast her ballot.
Opinion polls released a week ago had put them neck-and-neck. The results are expected to come in as early as Wednesday morning.
One minor presidential candidate, Dr Ekuru Aukot, was stranded for hours at Nginyang Police station after heavy floods washed away a bridge that was the only access to his polling station. An election in 2007, widely believed to have been flawed, touched off bloodshed that left at least 1,300 people dead and 600,000 displaced. About 45 percent of registered voters are under the age of 35.