The court then ordered a re-rerun election for October.
The opposition leader, Raila Odinga pulled out of the re-run after the Supreme Court annulled the result of the original 8 August poll after finding irregularities and illegalities when current President Uhuru Kenyatta was declared the victor.
Chebukati's sentiments came in the wake of the resignation of one of the seven electoral commissioners, Roselyn Akombe, plunging the country into further political uncertainty.
Opposition leader Raila Odinga had petitioned the court to overturn the result, claiming hackers infiltrated the commission servers and altered the results in favor of Kenyatta.
Wafula Chebukati, the Chairman of the Independent Electoral and Boundaries Commission (IEBC), said he will not continue to be pushed by majority commissioners to accept legal opinions that serve partisan interests that are not grounded in the constitution of the law.
"It would, therefore, have been logical for the Commission to be frank with the Kenyan people and clearly state the challenges we face in organizing a free, fair, and credible election", she added.
"The commission in its current state can surely not guarantee a credible election on October 26. I do not want to be party to such a mockery to electoral integrity", she said in a statement on Tuesday night.
Kenyatta vowed Wednesday that he will take part in the election even if he runs unopposed. Youths have also broken up meetings by election officials in the opposition stronghold of western Kenya this week.
Akombe urged Kenyans to remember the violence that followed a disputed 2007 poll, when more than 1,200 people were killed.
At least 37 people have died in violence since the August vote, although rights group say the actual number killed may have been double that total.
However, in a tweet, the electoral commission said it regrets Dr Akombe's resignation and will issue a detailed statement on the issue in due course.
But Kenyatta said in a televised speech on Wednesday: "We walk towards the declared date of the 26th of October both as a God-fearing leadership and government".
In an interview with the BBC, Akombe said she had received numerous threats while in Kenya and did "not feel safe enough to be able to go home".
A week before the August poll, the election commission's head of IT was found tortured and murdered in Nairobi, raising fears of a possible hack of the commission's computer systems. Tweeting on Wednesday, Ruto criticized the election board head's comments: "Chebukati should stop lecturing us and oversee the elections".