The commission's latest tally of ballots from 40,333 of the country's 40,883 polling stations show Kenyatta has 8.13 million votes, compared with 6.73 million for Odinga. "People want to see justice".
Meanwhile, International election observers Thursday called for restraint as Kenyans await the announcement of the official results from the nationwide polls.
The opposition's claim led to sporadic outbreaks of violence.
Odinga called the partial results "an attack on our democracy". One must win more than 50 percent of the votes that were cast Tuesday to avoid a runoff election.
"Hacking was attempted but did not succeed", Commission Chairman Wafula Chebukati told reporters at a news conference in the capital of Nairobi.
However, it admitted that a lack of mobile data coverage had delayed the delivery of the supporting documents, forms 34A and 34B.
"This is why Chris Msando was assassinated, so that this could happen", he charged. And as long as it's done appropriately, you have an ability to have full integrity of this election.
The foreign missions said they have worked hand in hand with the Kenyan people and with Kenya's institutions to prepare for free, fair, credible and peaceful elections.
"People are demonstrating due to their rights", said Edwin Onyango, a supporter of the 72-year-old Odinga, a former prime minister who has run unsuccessfully for president on three previous occasions.
Police fired tear gas on Wednesday (August 9) in the western Kenyan city of Kisumu, a stronghold of opposition leader Raila Odinga. President Kenyatta, the 55-year-old son of Kenya's founding president, beat him in the last election in 2013, but their rivalry is generations old - their fathers were political opponents in the 1960s.
"These results are not coming from out of the blue, but by fact and you can not claim that results are fake with respect to presidential and you welcome the areas where your governors and your members of parliament have won convincingly".
Kenya's opposition coalition the National Super Alliance on Thursday demanded its candidate Raila Odinga be declared president, claiming it had evidence he had won this week's election.
"The IEBC has put in place and has thus far followed a detailed process of paper ballot counting and security which, if followed through to the final steps, can give every Kenyan confidence that their vote was properly recorded and therefore this election can appropriately certify the outcome", Kerry said.
Even so, we note that some legitimate questions have been raised over the vote count and tallying.
Kenyatta is already on track for a win (97 percent of stations reporting, Kenyatta: 54.32 percent; Odinga's 44.8 percent).
Kenyatta supporters point to solid economic growth during his term, including massive infrastructure projects like a $4 billion railway financed by China.
"Many people turned up at the polling stations very early and with the aid of the electronic system made available, the process seemed to have been pretty smooth and fast".
Former US Secretary of State John Kerry, who is leading a group from the Carter Center, an worldwide democracy promotion group led by former President Jimmy Carter, told journalists: "We believe the IEBC put in place a detailed, transparent process of voting, counting, reporting and securing the vote, all of which lends significant credibility and accountability".