Preliminary results on Thursday had put Kenyatta at 54.2 percent of the vote and Odinga at 44.9 percent.
Electoral commission Chairman Wafula Chebukati has rejected the opposition's argument, however, saying the evidence they provided is "obviously and plainly falsified and contains elementary errors".
Over 400 worldwide election observers - including officials from the United States and the European Union - were deployed across the country to monitor voting, the tallying process and part of the post-election period.
Earlier, Mr Odinga's supporters said he had won, and published their own figures.
More than 1,000 people were killed in a campaign of ethnic violence in the months after Odinga, defeated by then-President Mwai Kibaki, claimed the vote was rigged. "I therefore wish to declare Uhuru Kenyatta.as President-elect", said Mr Chebukati.
After the mysterious murder and torture of a high-ranking elections official late last month, Odinga claimed that - in Eyder's words - "a hacker used that man's credentials to go into the electoral reporting system and changed the result".
"Going to court for us is not an alternative", Orengo says.
"Let us be peaceful. there is no need for violence".
Uhuru, 55, starts his second term as the fourth President of Kenya after a neck and neck race with NASA's presidential candidate, 72-year-old Raila Odinga. "At the end of the day we shall do an audit and those questions will be answered", he said. He added though, that the opposition doesn't plan on contesting the vote in court.
"If they can open those servers, and we all look at it, we are prepared to accept the results of what is contained in those servers", James Orengo, chief election agent for the National Super Alliance opposition coalition, told reporters.
In recent days, opposition officials have described the election results as a fraud and claimed that Raila Odinga, the 72-year-old Nasa leader, was the legitimate victor.
"The world is waiting for the final declaration of the election and the reactions", said Mr, Obasanjo.
Supporters of Kenyan opposition leader Raila Odinga are rioting in a Nairobi slum and in Kisumu, a city where he has strong support.
Uhuru, who is the sitting President of the Republic of Kenya, was declared victor together with his running mate William Ruto despite contests by the opposition that the election had been rigged. Results could be announced within hours, though the election commission has until Tuesday to do it.
The electoral commission admitted that hackers had tried to access its database, but said they did not succeed. Most of the country has remained calm.
Many Kenyans have left Nairobi in recent days, bracing for violence.
Violence broke out this week in some opposition strongholds in parts of the capital, Nairobi, and elsewhere.
Protracted turmoil could derail an economy that's grown an average of 5.7 percent a year since Kenyatta took power in 2013, and threaten its reputation as a top African investment and tourist destination.