President Uhuru Kenyatta said the presidential re-run, which was expected to be a run-off between Odinga and himself, would go ahead as scheduled despite his rival's withdrawal, Reuters news agency reported.
Odinga takes his complaints to the Supreme Court. "We believe that all will be best served by NASA vacating its presidential candidature in the election".
"Instead, the case for proceeding with the fresh election on 26 October without these changes is being made on the grounds of time constraints", added Odinga.
Kenya's Supreme Court last month overturned the August election of President Uhuru Kenyatta citing "irregularities" in the counting of results.
"It is his democratic right not to participate", Kenyatta said.
"The only election Jubilee administration is interested in is one that it must win, even unlawfully", he said.
Additionally, the former Prime Minister and his running mate accused IEBC CEO Ezra Chiloba, the "coup plotter in chief" of still standing in the way of a free and fair elections.
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It said while the United States did not back any party or candidate, it fully supports the work of an election board.
Kenyatta said he was not deterred by Odinga's decision.
Supporters of Odinga have been holding weekly demonstrations against the electoral commission in the capital, Nairobi, as well as in their strongholds of Mombasa and the western city of Kisumu.
"And the people of Kenya will have the right to choose and determine who their leader shall be", he said.
The Supreme Court which invalidated the August 8 polls during a September 1 ruling ordered that IEBC to conduct repeat polls within 60 days, after ruling that the August 8 polls were full of irregularities.
The uncertainty has also hamstrung east Africa's largest economy, leading to a slowdown in business across the private sector.
"Following the withdrawal of the NASA presidential candidate, the commission and the legal team are meeting and will communicate way forward", the poll body said. It also tweeted a letter it sent on Tuesday to Odinga's opposition coalition saying that "we have taken the necessary steps to guarantee the integrity of the fresh presidential elections".
According to figures released by IEBC chairman Wafula Chebukati, the incumbent garnered 8,203,290 votes while Odinga managed 6,762,224 votes.
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