Kenyan law states that electronic reporting must be double-checked and verified by physical paper forms signed by polling station officials before Kenya's Independent Electoral and Boundaries Commission, or IEBC, can declare a winner.
Odinga claims the election was rigged in favor of Kenyatta, saying he doesn't "trust" the paper forms that could have been "manipulated already."
At a news conference Thursday, members of Odinga's party gave no evidence to back up his claim, citing only unnamed sources at the IEBC.
While the challenger claimed election fraud, former US Secretary of State John Kerry tried to reassure Kenyan voters their election wasn't rigged.
Kerry: Every Kenyan's vote is protected
On Thursday, Kerry said he was confident in the integrity of the Kenyan elections and praised the country's election commission for its transparency and diligence.
The 73-year-old Kerry is co-leading the Carter Center's mission of election observers, who released their preliminary observations a day after Odinga claimed early electronic election results had been compromised
"The process is still underway. But we believe that the election's commission in Kenya has put together a process that will allow each and every vote's integrity to be proven," Kerry said, noting that there were "little aberrations here and there."
He reiterated that the IEBC is still working to verify the electronic online reporting with the physical ballot forms from polling stations, as required by law.
"If anything was electronically fiddled with, there is a way to go back and absolutely ascertain what happened in the polling station," he said. "So by paper ballots, there is a protection of each and every Kenyan's vote."
Fears of 2008
Odinga's complaints of election irregularities have stoked fears of aggrieved supporters taking to the streets in a scenario reminiscent of violence that erupted in the aftermath of the December 2007 election.
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.
Odinga's opposition party, the National Super Alliance, has repeatedly called for calm as the final results are compiled.
"We do not want to see any violence in Kenya. We know the consequences of what happened in 2008 and we don't want to see a repeat of that anymore," Odinga told CNN on Thursday.
"I don't control anybody. What is happening is that people just want to see justice. We also hope that the security forces are not going to use excessive force."
The election in Kenya, the biggest economy in East Africa and a regional hub, was peaceful and enthusiastic on Tuesday.
But confrontations emerged a day later between police and protesters in opposition strongholds in the capital and the western city of Kisumu, leaving at least two people dead.
On Thursday, Nairobi appeared to be somewhat quieter than usual, possibly because of school holidays and some concern from residents about potential violence. But people were returning to their daily routines after the national holiday on Tuesday, and some businesses were open.
Over 400 international 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.
Marietje Schaake, the head of the EU's mission, said Thursday that the group had seen "no signs of centralized or localized manipulation" after assessing voting procedures.
Failed attempt to hack system
Wafula Chebukati, chairman of the voting authority, confirmed Thursday that there had been an unsuccessful attempt to tamper with its election system.
"The commission has responded to the claims by (the National Super Alliance). Preliminary reports show hacking was attempted but did not succeed," Chebukati said, without elaborating further on the failed hack.
Odinga, a 72-year-old former political prisoner who was running for president for a fourth time, had flatly rejected the preliminary results as "fake" the day before.
He said hackers had infiltrated the election authority's systems using the identity of Chris Msando, an election official who was tortured and murdered
a week before the vote.
"What the IEBC has posted as results of the Presidential Elections is a complete fraud based on a multiplier that fraudulently gave Uhuru Kenyatta votes that were not cast," he said in a series of tweets.
"We have uncovered the fraud. Uhuru must go home," he added. "The IEBC must be fully accountable."