Long queues are reported nationwide as Kenyans vote in an election that observers describe as the most important in the country's history.
Polls were due to close at 17:00 (14:00 GMT) but officials said those in queues at that time would be allowed to vote.
There has been violence around the port town of Mombasa, with at least five police officers killed in one attack.
Authorities have urged Kenyans to avoid the widespread bloodshed that followed the disputed 2007 election.
More than 1,000 people died in ethnic and political violence following claims the poll had been rigged.
One of the frontrunners in the presidential poll, Uhuru Kenyatta, is due to face trial at the International Criminal Court (ICC) next month in connection with the 2007 violence - he denies organising attacks.
His main rival is Prime Minister Raila Odinga, who says he was cheated of victory last time.
Biometric kits fail
As thousands continued to queue to cast their ballots, voting was extended by up to seven hours to cope with long queues at polling stations.
Kenya's Independent Electoral and Boundaries Commission (IEBC) issued a notice via social media saying: "We wish to inform members of the public that all Voters on the queue by 5:00pm will be allowed to vote.
"Polling Stations that opened late will also close late to compensate for lost time."
The electoral commission said some delays were caused by a new system intended to reduce fraud, which observers hope will prevent the kind of widespread ethnic violence that followed the last poll in 2007.
After he cast his ballot, Mr Odinga said he would accept defeat - but added that he was confident of victory in the first round.
"I will congratulate the winner," he said.
Mr Kenyatta also sounded a conciliatory note, saying the president would represent the whole country and that any disputes should be taken to court.
Reports from around the country suggested long queues of voters had formed even before polling stations opened - and some voters, such as those in Eldoret, were waiting up to 10 hours to cast their ballots.
Some technical difficulties were reported with newly instituted biometric voting kits - designed to counter claims of vote-rigging and long delays in announcing poll results that were partly blamed for the violence in 2007.
In places, electoral officials are having to use the manual voter registers, delaying voting. But Lilian Mahiri-Zaja, vice-chair of Kenya's independent electoral commission, said the registers were complete and there was no reason why the election should not be credible.