With 80% of results in he has 55% of the vote against 44% for his rival, Raila Odinga, figures show.
However, the opposition coalition has rejected the partial results, saying election officials have not produced documents to prove their validity.
"They are fictitious, they are fake," said Mr Odinga.
"We have our projections from our agents which show we are ahead by far," he added.
The electoral commission is urging people to wait calmly for full results.
Many fear a repeat of the violence that followed the disputed 2007 election when more than 1,100 Kenyans died and 600,000 were displaced.
"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.
Voting passed off largely peacefully and some polling stations remained open after the scheduled 17:00 (14:00 GMT) closing time.
Mr Kenyatta is hoping for a second term in office.
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.
Scenes from the polling station
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.
-BBC