Mr Lawan met with President Bola Tinubu and Vice President Kashim Shettima in Abuja.
Senate President Ahmad Lawan has debunked speculations that he may join the race for the position in the 10th Senate.
He said he was not interested in contesting for the position to succeed himself.
Mr Lawan stated this Thursday while speaking with journalists after a meeting between the leadership of the National Assembly and President Bola Tinubu at the Presidential Villa in Abuja.
The meeting was attended by Vice President Kashim Shettima and Speaker Femi Gbajabiamila of the House of Representatives.
He stated that he never showed interest in joining the race because he does not wish to become the next senate president. He said after 24 years in the National Assembly, he has the responsibility to help newly elected lawmakers.
Mr Lawan was first elected into the House of Representatives in 1999 before he moved to the Senate.
"I don't really wish to be one. I have played my part and I am happy that we have played our part," Mr Lawan said in response to a question asked by a journalist. He added that "I have never indicated interest to run."
On the election of the leadership of the 10th National Assembly, he said there is a need to carry everyone along.
He said there are some issues that must be addressed, adding that the election of the leadership must be based on national interest and the interest of the National Assembly.
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"What will inform the emergence will be the national interest, interest of the National Assembly. Therefore, everybody matters in this process.
"We also believe that Mr President, having been a senator himself and his vice president (Kashim Shettima) also having been a senator, this is something that they will always wish and pray for.
"As the chairman of the 9th National Assembly, I find it dutiful and necessary to work with all the major stakeholders especially the leadership of our country, Mr President and to give my necessary opinion and advice on how the new leadership of the National Assembly should emerge and what we need to do to ensure stability and productivity of the National Assembly and to ensure a peaceful atmosphere between the legislature and the executive arm of government.
"We are getting somewhere and my prayer is that we are able to resolve all the outstanding issues by the grace of God. And Mr President is positively disposed to everything being done smoothly," he said.
The current 9th National Assembly will end on 11 June while the 10th session will commence on 13 June after the proclamation by President Bola Tinubu.
The next senate president will be elected on the day of inauguration.
Among those in the race for the presidency of the 10th Senate is a former governor of Akwa Ibom State, Godswill Akpabio; a former governor of Zamfara State, Abdulaziz Yari, incumbent Senate Whip, Orji Kalu, and the senator-elect for Imo West, Osita Izunaso.
Mr Akpabio has, however, been endorsed by the APC national leadership for the position and is also believed to enjoy the support of President Tinubu.
