With about a third of polling stations reporting, Deputy Prime Minister Uhuru Kenyatta held an early lead over his main rival, PM Raila Odinga.
The head of the electoral commission emphasised these were provisional figures and urged Kenyans to wait patiently for the final outcome.
In 2007, more than 1,000 people were killed in post-election violence.
Clashes broke out then after Mr Odinga claimed he had been cheated of victory by supporters of President Mwai Kibaki.
Violence has also marred the current election, with at least 19 people killed.
These [irregularities] we find to be placing in jeopardy the credibility of this process”Frank BettCoalition for Reform and Democracy (CORD)
By early Tuesday, Mr Kenyatta of the Jubilee alliance had established a lead over Mr Odinga, who heads the Coalition for Reform and Democracy (Cord).
With 34.4% of polling stations reporting at 10:30 Nairobi time (07:30 GMT), the 51-year-old deputy prime minister had 2.19m votes, or 55%, while the 68-year-old prime minister had 1.65m, or 41%, said the website of the Independent Electoral and Boundaries Commission (IEBC).
Analysts cautioned that early counting favoured Kenyatta strongholds.
The next nearest challenger was Musailia Mudavadi, of the Peace coalition, who trailed far behind with 113,955 votes, or 3%.
None of the other five candidates for the presidency had more than 1%.
The IEBC has warned that counting might not be completed until Wednesday.
The winning candidate must get
50% of the total votes cast + one vote
At least 25% of votes in half of Kenya's 47 counties
If there is no clear winner, a second round of voting will take place, probably on 11 April
Mr Kenyatta is due to stand trial at the International Criminal Court (ICC) in August for his alleged role in the 2007 unrest, when supporters of the rival candidates, from different ethnic groups, took up arms against each other.
Mr Odinga later joined a government of national unity under a peace deal.
The US and other Western allies of Kenya have warned of possible "consequences" if Mr Kenyatta wins.
However, Mr Kenyatta's running mate, William Ruto, who also faces charges of crimes against humanity, insisted on Monday that they would be able to discharge their duties if elected and would co-operate with the ICC to clear their names. Both deny any wrongdoing.
The BBC's Gabriel Gatehouse visited a polling station as people queued
Long queues were reported outside polling stations across the country on Monday as Kenyans chose a president, as well as members of parliament and senators, county governors, women members of 47 county assemblies, and civic leaders.
Raila Odinga vs Uhuru Kenyatta
Uhuru Kenyatta
Son of Kenya's first president, Jomo Kenyatta
Due to stand trial at ICC in April accused of organising violence in last election
His running mate, William Ruto, also accused
Both deny the charges
From Kikuyu ethnic group - Kenya's largest at 22% of population and powerful economically
Kikuyus and Ruto's Kalenjin community saw fierce clashes after 2007 poll
Currently deputy prime minister
Raila Odinga
Raila Odinga son of first Vice-President Jaramogi Oginga Odinga
Distant relative of Barack Obama
Believes he was cheated of victory in last election
From Luo community in western Kenya - 11% of population.
Some Luos feel they have been marginalised by central government
Third time running for president
Currently prime minister under power-sharing deal to end violence last time
The head of the IEBC said turnout among the 14.3 million voters was more than 70% - marginally higher than in 2007 - but did not give a precise total because many polling stations stayed open late into the night.
The IEBC said some delays were caused by difficulties with newly instituted biometric voting kits intended to reduce fraud.
Some observers are concerned about ethnic and political violence erupting should neither of the two front-runners poll more than 50% - in which case the vote will go to a run-off, probably on 11 April.Machete attack
After the polls closed, Mr Ruto said he believed the elections had been "free, fair and credible".
However, Mr Odinga's party warned that there had been irregularities which placed "in jeopardy the credibility of this process".
Frank Bett, a senior CORD official, said there had been reports of late voting at one polling station hours after polls closed officially, people casting more than one ballot, and failures of the biometric kits in some places.
The IEBC earlier acknowledged that a polling clerk had issued extra ballots, and paper voter lists had been used when the electronic registration system failed.
Among the 19 people killed were four policemen who were attacked with machetes in the coastal city of Mombasa by suspected members of the separatist Mombasa Republican Council (MRC), which had demanded the elections be scrapped.
The group's spokesman denied it was responsible, but police Inspector General David Kimaiyo said they were planning a raid that would "see the end of the MRC".
Police also blamed the MRC, which believes Kenya's coast should be an independent country, for three deadly attacks in the nearby town of Kilifi.
Gunfire and explosions were also reported in the town of Garissa, near the border with Somalia. Gunmen stormed two polling stations after voting ended, but were forced to retreat by security forces, the deputy speaker of parliament told Associated Press.
