Akeredolu said it was unnecessary to recognise Tinubu alone when the party has over 30 national leaders apart from Buhari and Odigie-Oyegun.
Akeredolu said mentioning Tinubu's name means he has to acknowledge about 36 other leaders of the party.
He stated this at the Presidential Villa in Abuja on Wednesday, November 30, while addressing newsmen.
He said there was no need to be "looking for leaders all over the place" having acknowledged President Muhammadu Buhari for the role he played in his emergence, and John Odegie-Oyegun, chairman of the party "for standing by the truth."
He said: "I thanked the president of the Federal Republic of Nigeria and the leader of our party profusely for the leadership that he showed leading to this election.
"I also thanked our indefatigable chairman for standing by the truth and for his position on this matter that led to this election. I have no reason to do otherwise.
"You see, party structures to the best of my knowledge is very clear. You have the leadership of the party and that is represented by Chief John Odigie-Oyegun. And after the election, a chief executive emerges, he becomes a leader of the party, you don’t have to personalise and be looking for leaders all over the place.
"If we have to do that then I will have to mention 36 or 37 leaders. So I believe the leadership as represented by the president covers all leaders and that tells me it would include Chief Bola Ahmed Tinubu, it would include even Baba Akande, Onu, so many leaders. But president Buhari is the leader of the party so that is my position there."
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On his relationship with Tinubu, Akeredolu said, "The relationship with Asiwaju Bola Ahmed Tinubu has always been the same. I don’t think we have any strain relationship.
"For me as a person, I believe he is one of the leaders of the party and I don’t see any strained relationship between us. And you would observe that he has sent in his congratulatory message after the election, so what else do you expect? I mean all of us see this as victory for the APC, not for Akaredolu, not for an individual but for the party as a whole. I believe he is a member of the party. Mr. Femi Adesina had issued a release but you journalists just want to put words into our mouths."
Reacting to the defection of a PDP senator from Ondo, Yele Omogunwa, to the APC, Akeredolu said the lawmaker had joined the ruling party before the election but only made it official on Wednesday.
The governor-elect reiterated his earlier position on not probing the outgoing Governor of Ondo state, Olusegun Mimiko, but he said if a monumental fraud is discovered like "Dasukigate", "the law of the land will take its course."
He said: "At the centre the government of the President Muhammadu Buhari said we must look back in order to move forward, he has been there for over a year now, has he instituted a probe?"
"Looking back is not a probe and I maintain that I will not probe any regime. This is a responsible leadership and I’m elected to lead the people.
"The task ahead of us is enormous than for us to start instituting probes. My own is not to institute any probe of last regime and that is what President Buhari has done. But if we find out that wrongs were committed we have enough laws of the land to take care of people who have committed wrong. As we start our work as we go ahead if there is any semblance of Dasukigate at the state, the law will take its course; that is different from probing. We will follow what Mr. President is doing at the centre."
The Independent National Electoral Commission (INEC) on Sunday, November 27, declared Akeredolu winner of the Ondo governorship election.