Odinga's NASA party announced at a news conference Wednesday that it will not participate in the October 17 election without major changes to the IEBC.
"(The board's) disobedience of this 28 Aug order in critical areas leaves us with no option but to accept the petitioner's claim that the (election board) system was infiltrated and compromised and. data interfered with", said Judge Philomena Mwilu.
In addition to the technology problems, opposition candidate Raila Odinga - set to contest the election against Mr Kenyatta - has said he will not take part in the re-run unless members of the country's electoral commission are replaced.
Kenya has the region's richest economy and is a key Western ally in a region often shaken by violence.
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Fresh elections will be held in the country on October 17.
Separately, a French company that provided equipment for last month's elections says the biometric and results transmission equipment would not be ready for the new vote next month because it would have to be reinstalled.
"Since the Supreme Court delivered judgment. these threats have become more aggressive", Maraga said in a briefing with reporters outside the court, adding that individual judges and their staff have become subject to numerous threats on social media.
The company provided two electronic systems that identified Kenyan voters and transmitted election results from nearly 41,000 polling stations to a central tallying center.
Addressing the court, Judge Mwilu said the electoral body had refused to comply with court orders to open its computer servers, saying this suggested that opposition claims of tampering could be true. "Failure by the board to do as ordered must be held against it".
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The election was also notable for the role played by Hafiz Muhammad Saeed , one of the most-wanted militant leaders in South Asia. Mr Sharif has always denied any wrongdoing but the Supreme Court recently dismissed petitions seeking a review of that decision.
Kenyatta says his criticism of the Chief Justice should not be viewed as an attack on Maraga's Kisii community.
Also on Tuesday, police also used tear gas to disperse supporters of the ruling party protesting outside the Supreme Court.
The four judges who decided in a majority decision to annul the vote also said the election commission had failed to verify the numbers before declaring Kenyatta victor.
President Uhuru Kenyatta promised to respect the ruling although he has repeatedly criticised it harshly.
Chief Justice David Maraga said if the president was "tired" of having a "strong and independent" judiciary, he was free to call a referendum to abolish it.
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