Provisional results released shortly after the polls on Tuesday suggested Kenyatta, in power since 2013, was the victor by a substantial margin.
"The commission has done its best to ensure a credible election", said Chebukati.
But the opposition coalition rejected the commission's announcement before the results were declared, calling the process a "charade".
Protests have erupted over several days in opposition areas after Odinga alleged vote-rigging in Tuesday's disputed election.
Kenyatta said he wants to work with Odinga: "I reach out to you. We have been there before", he said.
"We are very grateful that we were able to participate in the elections successfully and peacefully".
A resident of Nairobi's Kawangware slum said police fired tear gas at dozens of Odinga supporters throwing stones on Thursday. We shall go into that and find out whether those claims are true.
"We need to be calm, we need to be sober ... this is moment for peace", he added.
Msgr. Wilybard Lagho, vicar general of the Mombasa Archdiocese, said the election commission had approached the church about offering polling stations, and church officials agreed.
He has urged the IEBC to conduct the tallying process in an effective and transparent manner within the legally stipulated timeframe and, where necessary, to engage in dialogue with political actors before the official announcement of results.
Tuesday's contested vote has caused tension across Kenya as hundreds of riot police patrolled the capital Nairobi. "At the end of the day we shall do an audit and those questions will be answered", he said.
Kenyatta's administration has also been plagued by allegations of corruption that many Kenyans see as the reason for the country's vast inequalities, with well-connected millionaires enjoying luxuries while large numbers of people struggle to afford food and housing.
Odinga also said that hackers gained access to the election computer system by using the identities of Chebukati and Chris Msando, its technology manager who was tortured and murdered in late July, to manipulate the outcome, and that his party had obtained its own data from sources within the commission showing he had won.
The head of the European Union delegation, Marietje Schaake, said her team had seen no signs of "centralised or localised manipulation" of the voting process but that there were concerns about the misuse of public funds at local and national levels by all parties.
In the southeastern Tana River region, police said five men armed with knives had attacked a vote tallying station and stabbed one person to death.
The declaration was boycotted by representatives of the opposition coalition, led by Raila Odinga.
Between Dec. 28, 2007, and February 28, 2008, at least 1,000 people died and 600,000 were displaced from their homes, after President Mwai Kibaki was declared the victor and Odinga rejected the polls as rigged.
The election is a test of democracy in the East African economic power.
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