The lawmakers say the meeting centred on the issues facing the country, particularly the economy and social challenges.
President Bola Tinubu Thursday met with his preferred candidates for the positions of speaker and deputy speaker, Tajudeen Abbas and Ben Kalu, as the race for leadership positions of the 10th House of Representatives thickens.
Mr Tinubu had endorsed the duo while he was still the president-elect. However, several aggrieved aspirants in the race have rejected the endorsement.
The aggrieved aspirants include incumbent Deputy Speaker Idris Wase, Yusuf Gagdi, Muktar Betara, Sada Soli, Miriam Onuoha and Aminu Jaji. They have remained in the race and vowed to present consensus candidates to challenge Messrs Abbas and Kalu.
With the inauguration of Mr Tinubu, it remains unclear the level of influence he may exert on the election of the leadership of the 10th Assembly.
Briefing journalists after the meeting, Mr Abbas said it was strictly centred on the issues facing the country, particularly the economy and social challenges. He further stated that the discussion did not extend to the other aspirants.
Mr Abbas said he had not been able to meet with the president since the latter was sworn in on Monday.
"We did not discuss our opponents who want to be speaker or deputy speaker. We restricted our discussion to the matters of the day, issues that have to do with the challenges this country is facing, particularly the economic and social challenges. And what he intends to do in the next few days, particularly what he has done on the issue of fuel subsidy," he said.
Mr Abbas also dismissed the tag of "rubber stamp" on the current National Assembly, stating that the 9th Assembly remains the best ever.
"I will want to go back to history. Even the people not endorsed by the government of those days, have they done better than the leadership of the 9th Assembly which we believe was the first time the thinking of the legislature and executive were in sync.
"Whoever is talking about rubber stamp assembly does not know about the working of the National Assembly," he said.
In his remark after the meeting, Mr Kalu also dismissed the tag of a rubber stamp on the outgoing parliament, stating that the inter-dependence of the two arms -- legislature and executive -- cannot be ruled out.