Odinga has also rejected early results from Tuesday's vote indicating a strong lead for President Uhuru Kenyatta.
"We urge political parties and candidates to remember that Kenya and Kenyans matter more than any candidate, party or election, and to refrain from actions or statements which could heighten tension whilst the country awaits the vote outcome", Stewart said in a statement issued on Thursday night.
Opposition official Musalia Mudavadi claimed to have "complete data" from election commission servers showing Odinga with a lead of several hundred thousand votes over Kenyatta, contrary to results on the commission's website that put the president more than 1 million votes ahead.
The IEBC Chairman Wafula Chebukati also added that the only declaration they will make will be from polling station results.
"They loaded an algorithm which is a formula to create a percentage gap of 11 percent between our numbers", Odinga continued, referencing the gap between himself and president Kenyatta at the time.
But there were clashes in his hometown of Kisumu, with police firing tear gas at protesters.
At least six people have been killed in protest violence, Aljazeera reports, and onlookers fear a repeat of post-2007 election violence which saw over 1000 people killed in the months following the elections.
Mudavadi says there is a "serious attempt to try to either doctor or alter the final results".
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Winds in the tropics and warmer-than-expected tropical waters are ideal for hurricane formation this year, according to NOAA. The storm made landfall early Thursday as a Category 1 hurricane, the first of the Atlantic hurricane season.
Odinga ran in Kenya's previous two elections and lost both, blaming vote rigging following irregularities at the polls.
The commission said Kenyatta won Tuesday's election with 54 percent of the vote.
A senior police officer, who spoke on condition of anonymity, confirmed that two people had been killed in the slum of Mathare in Nairobi on Wednesday.
Mr Odinga had said hackers could have used the identity of a top election official, who was tortured and murdered days before the vote.
Mr Odinga, 72, draws support from the Luo tribe, Kenya's second-largest ethnic group. More than 19.6 million registered voters went to the polls on August 8 in a tightly-contested election that has drawn the attention of the world. One injured man in Kawangware was carried away by protesters who said police shot him.
When asked at a press conference how he knew about the hacking of the election database, Odinga said he couldn't reveal his source.
He says he will not accept the results, calling them "fake" and a "sham", claiming that a hacker took control of the Independent Electoral and Boundaries Commission (IEBC) system early in the morning and manipulated results.