Kenyatta was leading with 55 percent of the vote to Odinga's 44 percent in results released by the electoral commission (IEBC), but with just 9,405 of the country's nearly 41,000 polling stations counted, it was too soon to tell if the incumbent's lead would hold.
Emotions are high after a bad-tempered campaign marred by opposition claims of a plot to rig the vote, and counting is considered the most sensitive part of the process in a country with a history of post-poll violence.
More than one-and-a half million votes had been tallied in the presidential vote, but as night fell some were still voting due to delays and long queues.
Today's elections took place a decade after a shambolic 2007 vote -- which foreign observers agreed was riddled with irregularities -- sparked violence which left more than 1,100 people dead and 600,000 displaced.
People stood patiently for hours in snaking queues around the country for a vote that went off peacefully, despite reports of some technical glitches and delays.
"I also want to say that if I lose, I will accept the will of the people," Kenyatta said after voting.
Odinga, 72, is taking his fourth and likely final stab at the presidency. He claims elections in 2007 and 2013 were stolen from him.
"In the unlikely event that I lose I don't need a speech, I will just speak from my heart," he said shortly before voting.
The IEBC electoral commission moved quickly to deal with any complaints, removing clerks in a polling station where ballot papers were pre-marked as "rejected".
IEBC chief Wafula Chebukati said voting had gone "smoothly" despite minor delays and technical hiccups at some polling stations.
In semi-arid northwest Turkana, flooding from heavy rain cut off roads and several polling stations had still not opened by closing time.
Odinga's National Super Alliance opposition coalition (NASA) released a statement praising poll officials and security forces.
"We commend them for the good job so far and urge them to keep it up," it said.
However, the coalition complained some of its voters had been turned away or their names were missing from the voters' register.
As vote tallying starts, the focus is on the electronic system in place to send results to Nairobi. The failure of this system in 2013 meant votes had to be counted manually, leading Odinga to cry foul.
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