Supporters of Kenya's National Super Alliance (NASA) celebrate after the Supreme Court ordered a re-run of the August 8 presidential poll in Nairobi.
The Supreme Court was established to rule on decisions of the country's appeal courts regarding the law or interpretation of the constitution and is the only court permitted to decide in disputes concerning the presidential election.
In the August election, Uhuru Kenyatta was elected with a little more than 54 percent of the vote, but the voting itself was marred by reports of irregularities, leading to the Supreme Court decision to order a new vote within 60 days.
The Independent Electoral and Boundaries Commission declared Kenyatta the victor last month by a margin of more than 1.4 million votes, with around 19 million eligible voters. Four of the high court's six judges ruled that the vote had been marred by irregularities that had harmed the integrity of the election.
Odinga called the move "precedent-setting" and historic for Kenya and the rest of Africa.
He said, "Why is it that this time they don't want to accept the ruling from the courts?"
Odinga called for the election commission to be disbanded.
"We urge everyone to work to make it free, fair, credible, and peaceful".
It was the first time a presidential election result was overturned in the continent and followed three previous failed bids by the 72-year-old Odinga for the presidency - in 1997, 2007 and 2013.
Spokesmen for both the president and the election board rejected the idea of changing the entire board.
"There will be no election on the 17th of October until terms and conditions which we have spelt out in this statement are met", a combative Odinga told reporters. However, Odinga said he wanted elections to be held on October 24 or 31, instead.
A spokesman for the electoral board, Andrew Limo, said the situation was complicated by the fact that the court would not release its full verdict until September 21.
He referred to Justice Maraga and his fellow judges as wakora (crooks in Swahili), saying they had "decided to cancel the election". She certainly understands her country much better than I do. If it turns out that the computerised vote tallying was seriously manipulated, the opposition will get a boost.