With a little more than 40% of the vote counted, Kenyatta was leading -- 53% to 42% -- over his main rival, Prime Minister Raila Odinga, according to the election commission website
If Kenyatta wins, he will find himself in an unusual quandary.
The current deputy prime minister, he has been indicted by the International Criminal Court for allegedly inciting a local militia to conduct reprisal attacks in the last election.
His running mate, William Ruto, also faces ICC charges at the Hague. Both have denied the charges.
Although Kenyatta has maintained an early lead since polls closed after Monday's election, it is still too early to declare a winner. Analysts have raised the possibility of a runoff.
The election carries significance far beyond its borders.
An Independent Electoral and Boundaries Commission officer shows presidential ballots in Ngong, Kenya, Monday.
As the largest economy in East Africa, Kenya is a crucial trade route into the rest of the continent and provides an important buffer of stability in a region that includes the fledgling Somali government and the politically tense Sudan and South Sudan.
Kenya is also a major U.S. ally in the war against Islamist militants in the region and has remained relatively peaceful amid civil wars in neighboring nations.
'Hiccups here and there'
Glitches with the new electronic voter system are slowing down the tallying, officials said.
The election commission urged citizens to be calm and patient, hoping to avoid tension and distrust in the system, which contributed to the postelection violence in December 2007.
"Sometimes a couple of computers would get kind of out of whack and would slow the process down," said Abdullahi Sharawi, a commissioner of Kenya's Independent Electoral and Boundaries Commission.
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The hitches are related to the new computer-based biometric identification, according to the commissioner.
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"Definitely, there is going to be some hiccups here and there, but I think, when you assess the whole, then we think the work, so far, is very good," he said.
United Nations chief Ban Ki-moon urged Kenyans to maintain peace.
"I have been encouraged thus far by the largely peaceful and orderly process, despite some incidents of violence and some technical problems," he said.
Eager to avoid a repeat
Kenyans are eager to avoid a repeat of the last election in December 2007.
At the time, the nation plunged into ethnic violence after Odinga disputed results that declared incumbent president, Mwai Kibaki, as the winner, alleging the election had been rigged.
Protesters took to the streets, where supporters of both camps fought one another.
More than 1,200 people were killed and hundreds of thousands displaced -- the worst violence since the nation gained independence.
While the poll has been relatively peaceful this time, authorities said at least 10 people were killed in isolated incidents in the coast.
Leading up to this election, the candidates declared they would settle any election disputes in court and urged their supporters to avoid bloodshed at all costs.
After the disastrous poll, the government set up an ambitious new constitution, making this election one of the nation's most complicated polls since the country gained independence from Britain in 1963.
It also revamped various political systems, including the electoral process and the judicial system.
But analysts say the real test will come after the results are announced; will the loser bow out gracefully to avoid stoking tensions?
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Millions cast ballots
About 70% of the 14.3 million eligible voters voted this week, according to election officials. A total of eight contenders are vying for the presidency.
The winner must secure more than 50% of the vote to avoid a runoff tentatively scheduled for next month.