A large number of voters would be disenfranchised because opposition leader Raila Odinga, who withdrew from the new election after challenging the first one in court, wants supporters to boycott the vote while seeking electoral reforms, the petition says. Human rights activists have said police fatally shot 67 people since the results of the August election were announced.
The president's main rival Odinga has vowed that there would be no elections on October 26 and called for countrywide protests on that day.
The bodyguard of a member of Kenya's Supreme Court was shot and injured on the eve of its judgment about whether to suspend a controversial presidential election.
Kenyan President Uhuru Kenyatta on Sunday led the country in national prayers, calling on Kenyans to maintain peace ahead of the October 26 repeat presidential elections.
Odinga's supporters had also on Monday took to the street in the western city of Kisumu to protest against the re-run election.
The top court, whose surprise decision to annul the August 8 election over irregularities set the stage for this week's new vote, said it will convene Wednesday morning to hear petitioners who allege that Kenya's electoral commission is in disarray and prone to political interference.
India defeat Pakistan by 4-0 to reach Asia Cup final
However, the second quarter also remained goalless and both the teams went into the second half without opening the scoring sheet. The goals were scored by India's Harmanpreet Singh, Chinglensana Singh and Ramandeep Singh, while Ali Shan scored for Pakistan.
The board said it was impossible to meet other demands - such as changing the technology provider - in the short time frame allotted for new elections.
But last week electoral commission chairman Wafula Chebukati said "it's hard to guarantee a free, fair and credible election". She then fled to the United States, saying she feared for her safety.
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.
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.
Nasa presidential candidate Raila Odinga has said that he has not called for any demonstrations on Thursday.