Kenya's incumbent President Uhuru Kenyatta has taken an early lead as votes are counted after Tuesday's election.
With more than half the results in he has 55% of the vote against 44% for his rival, Raila Odinga, figures show.
Mr Kenyatta is hoping for a second term in office but faces a tough challenge.
Voting has passed off largely peacefully and the electoral commission has urged people to wait calmly for all the results.
"During this critical phase, we urge all Kenyans to exercise restraint as we await official results from the polling stations and indeed as they start trickling in," the commission said.
Many fear a repeat of the violence that followed the disputed 2007 election. More than 1,100 Kenyans died and 600,000 were displaced.
People began queuing early in the morning and even overnight to cast their votes
Some polling stations remained open after the scheduled 17:00 (14:00 GMT) closing time in areas where heavy rain and other problems had hampered voting.
Despite Mr Kenyatta's early lead, the BBC's Tomi Oladipo says it is too early to tell which way Kenyans have voted.
To win outright, a candidate needs more than 50% of the vote, and at least 25% in 24 of Kenya's 47 counties. If that threshold is not met, a run-off vote between the top two candidates will be triggered.
Voting for the national and local assemblies has also been taking place.
People started queuing early to ensure they could cast their vote. Long queues could be seen, and video footage at one polling station showed people injured after an apparent stampede.
There was also the failure of some voter-identification equipment and one in four polling stations were apparently without mobile phone coverage meaning that officials would have to drive to the nearest town to send results.
There were reports that one man had been killed in clashes in the Kilifi area.
But there was one heartening moment when a woman gave birth to a baby girl as she queued in West Pokot to cast her ballot. New mother Pauline Chemanang called the circumstances of the birth a "blessing" and called her baby Kura, Swahili for "ballot", according to local radio.
Election officials will be busy through the night counting the votes
Mr Kenyatta called on Kenyans to pull the country together
Mr Odinga has raised fears of vote-rigging
Casting his vote in his hometown of Gatundu, north of Nairobi, Mr Kenyatta said he would accept the outcome of the election.
"To my competitors, as I have always said, in the event that they lose, let us accept the will of the people. I am willing, myself, to accept the will of the people," he said.
Opposition leader Mr Odinga cast his ballot in the Nairobi slum of Kibera.
Speaking outside the voting centre, he told his supporters: "Let's turn out in large numbers and vote."
By Alastair Leithead, BBC News, Mathare
The queues were long and the voters impatient. Many arrived in the middle of the night to cast their ballots early and the electronic system is taking quite a while to verify voters.
If fingerprints don't register, ID card numbers have to be typed in to the electronic tablets and then there's a manual backup.
The responsibility lies with the Independent Electoral and Boundaries Commission to deliver a free and fair election.
The test will come when the polls close, the votes are counted and the results have to be transmitted to the tallying centres.
The presidential race is expected to be close.
Mr Odinga, 72, has run for president three times and lost each time. President Kenyatta, the 55-year-old son of Kenya's founding president, beat him in the last election in 2013, but their rivalry is generations old - their fathers were political opponents in the 1960s.
Mr Kenyatta and his running-mate William Ruto were indicted by the International Criminal Court for their alleged roles in the bloodshed a decade ago. The case ultimately collapsed due to lack of evidence, and after key witnesses died or disappeared.