Politics in Kenya is often split along tribal lines, with Mr Odinga - a Luo - and Mr Kenyatta - a Kikuyu - continuing a dynastic rivalry which began with their fathers after the country won independence from Britain.
The political stand-off has also blunted growth in East Africa's richest economy, a nation valued for its stability and relative freedom in a region plagued by conflict.
Human rights activist Khelef Khalifa, one of the petitioners, said Tuesday that the Supreme Court judgment nullifying President Uhuru Kenyatta's August re-election stated that the fresh election must be credible and verifiable.
Human rights activists have said police fatally shot 67 people since the August 8 election whose annulment by the Supreme Court opened the way to the new vote.
Last week, the head of the election board said it was not clear a free and fair vote could take place due to intimidation and political interference.
A petition seeking to have Super Alliance (NASA) leader Raila Odinga be forced take participate in the repeat presidential election set for Thursday has been dismissed by the High Court.
The Judge acknowledged that there is an active and critical ongoing presidential process in the country and if Pkosing's orders are granted, the court will be going overboard in determining the question of validity of the same process way beyond its jurisdiction.
Spain to dismiss Catalonia's government, call elections
Regional authorities said about 90 percent of those who cast ballots voted for independence. The referendum has been deemed illegal by the central Spanish authorities.
On Monday, the International Crisis Group, a global think-tank, called for a delay in the election.
On Tuesday, Nasa protesters were picketing towards the Nairobi CBD by 1pm.
"You see there are two forces here; those who want to go on with the sham elections irrespective of the consequences and those who are saying no it is not right to do it", he said.
Around him, marchers waved branches and blew whistles.
Kenyatta officially won the first election on August 8, by 1.4 million votes, but the Supreme Court annulled that outcome on September 1 over procedural irregularities.
His threats to boycott the election if certain conditions are not met, Mr Pkosing said, will be unlawful.
According to the constitution the vote must be held before 1 November.