Mr Akpabio told Governor Fubara not to struggle for political power if there was no benefit to it.
Senate President Godswill Akpabio and Governor Siminalayi Fubara of Rivers State have disagreed on the motives for power struggle among politicians in Nigeria.
Governor Fubara has been involved in a power tussle with his predecessor, Nyesom Wike, resulting in a crisis that split the state assembly into two factions - one loyal to Mr Wike, who is now the minister of FCT and the other loyal to Mr Fubara.
In his remark on Saturday at the funeral service of Herbert Wigwe, the late group chief executive officer of Access Holdings, Mr Fubara queried the motives behind political struggles and rivalries, which according to him, sometimes result in death.
Mr Fubara was addressing the congregants which included serving and former governors, financial and business leaders. The church service was streamed live on Facebook.
"This one has to do with our political class. What is all this struggle all about? You want to kill, you want to bury. What is it all about?" Governor Fubara queried, in a remark that was intermittently disrupted by applause.
Referring to the late banker, the governor said, "Here's a man, he's not a politician. He made his money through us - our investment. He has the world in his palm financially. He controlled even the political classes.
"But today, with all the powers financially, he couldn't control life."
Shortly after Governor Fubara's remark, Mr Akpabio, a former governor of Akwa Ibom State, walked up to the podium to make his remark.
Mr Akpabio once served as a commissioner before he became a governor in 2007.
In his remark, Mr Akpabio, apparently defending Mr Wike, recalled how he wanted to become the deputy governor of Akwa Ibom in 2006, but was dissuaded by then incumbent deputy governor, who told him the office has no "financial benefits."
Mr Akpabio was responding to a question raised by Governor Fubara on the motives behind the power struggle by politicians.
Mr Akpabio said to Governor Fubara, "I will answer you. We are not talking politics. In 2006, I wanted to become the deputy governor and the then-deputy governor invited me and said this office has no money, there is nothing in it. I don't know why you still insist on removing me from here and taking over," Mr Akpabio recalled.
"So, a woman who went with me said Your Excellency, don't wait for impeachment, just resign since there is nothing in it (the office).
"He (the deputy governor) stood up and started punching the woman. I said Your Excellency, don't punch the woman, she is telling the truth, there is nothing in it. That's why I want it because you are too big for it.
"Your Excellency, Governor Fubara, if there is nothing in the struggle, don't struggle."
Mr Wigwe, his wife, Chizoba and his son, Chizi died in a helicopter crash in the United States on 9 February.
Their remains were interred on Saturday at their country home, Isiokpo, headquarters of Ikwerre Local Government Area of Rivers State.