The All Progressives Congress has urged the Senate president, Bukola Saraki, to quit the office after he defected to the opposition.
Mr Saraki joined his former party, the Peoples Democratic Party on Tuesday, complaining about maltreatment in the APC.
Scores of his supporters, including Gov. Abdulfatah Ahmed of Kwara, have since joined him in the PDP.
The APC said Mr Saraki should act honourably and relinquish his position.
"But whatever is the reason, we can decamp from the party but we can't decamp from Nigeria. The only thing is that there are other consequential issues that every man or woman of honour, who had taken such decisions would be expected to follow through," party chairman, Adams Oshiomhole, told journalists Wednesday.
"I mean you should not collect a crown that belongs to a family and wear it on behalf of the family; if for your personal reasons, which he has enumerated that he has gone to another family, it is just a matter of honour to leave the crown in the house that the crown belongs to," he said, subtly challenging Mr Saraki to relinquish his position as senate president.
He made the comment after a meeting with President Muhammad Buhari.
Mr Buhari met the party's leaders and some senators on Wednesday to discuss the defections that have hit the party, before he proceeded on a vacation.
The meeting took place inside the president's office at Aso Rock Villa Abuja shortly after the meeting of the Federal Executive Council (FEC).
Briefing correspondents after the meeting, Mr Oshiomhole said it was held in response to the recent developments within the party.
Senate President Bukola Saraki, Governors Abdulfatah Ahmed of Kwara and Aminu Tambuwal of Sokoto states all dumped the APC and joined the opposition Peoples Democratic Party (PDP) between Tuesday and Wednesday.
Other notable members of the party including its spokesperson, Bolaji Abdullahi, also left the party.
Mr Oshiomhole said "nobody in the APC will be surprised about the development, in fact they (defectors) have stayed little bit longer than we thought".
Mr Oshiomhole said Governor Ahmed for instance "had last alluded that he would leave the APC, we are not surprised at all".
The APC chairman however, admitted that these are "tempting moments" for him because he had faced similar situations while he served as governor of Edo State.
"But the beauty of democracy is that, whether big or small, it is one man, one vote, on election day, no difference between a senator, a president, a journalist and any other person.
"In a sense, we have to accept that once a couple for any little reason or the other find that they not compatible, the only honourable thing is to go (separate)," he said.
He also said he was particularly happy that Mr Saraki, while defecting said he was leaving "not because the new leadership of the party did not make efforts to make him stop".
"He admitted that not only did I do everything possible along with the Vice President, along with some governors and we had meeting with the President, but he argued that those efforts came too late. But I couldn't have started acting before I was born.
Mr Oshiomhole said as it stands currently, "APC is still the largest party in the Senate, because it has 53 senators, more than the other parties".
"So, I think the important thing is that our democracy is still evolving, there are a couple of lessons to learn from the development. Going forward, we will expect the system to get stronger to the extent that it is able to learn the correct lessons and take the correct steps to profit from these developments.
"I have made this point and some commentators who don't seem to understand take one part of the argument and leave the other. I have said that if people have genuine, verifiable grievances, we are committed even now to listen and address those grievances in what I call, win-win manner.
"I have been consistent with that during the campaign, I have been consistent since I was sworn in, I have made the points in my acceptance speech, I have emphasised this when I met with the Senate caucus and speech, I have emphasised this when I met with the House of Representatives caucus, that we are ready to do justice to anyone who is genuinely aggrieved and whose grievances are such that we can deal with them provided we enthrone justice, fairness and all sides purge themselves of any arrogance.
"To the best of my knowledge, all senators, house of reps members were happy, the ones that are not negotiable, there is nothing we can do about it," Mr Oshiomhole said.
Also speaking, Senate Leader, Ahmed Lawan, said they came to see Mr Buhari before he proceeded on his vacation.
Senator Ahmed Lawan [Photo credit: Thenigerialawyer]
He said they discussed the issue of the budget of INEC for the 2019 election, which is a request by Mr Buhari to the National Assembly.
"I believe that we are going to do a lot of justice to the people of this country to work hard to pass those requests," he said.
Mr Ahmed also said the APC leadership will continue to "consult, unite and solidify" themselves.
He also said that the APC remains the majority in the Senate, saying "we have 53 senators, we reeled out the names and the states. Though the 'other side' are claiming they have 60, 70 but they have never given a name, it is left for you to make your judgement.
"In fact, I am using this medium to challenge the PDP senators, we have published ours and among the 53, none has come out to deny that he is in APC.
"Let them publish their own, they remain 48 senators in PDP. And by the grace of God, when the by-elections in Bauchi and Kaduna holds, we will get two more senators and that will boost our number," he said.
Pic 1. President Muhammadu Buhari (M) with APC National Chairman, Comrade Adams Oshiomhole (4th L) and the members of APC Senators after their meeting at the Presidential Villa in Abuja on Wednesday night 04018/26/7/2018/Callistus Ewelike/NAN
The official also said APC senators have "placed their total commitment and loyalty to the party and Mr Buhari".
"We remain true and genuine representatives of our people, we will not want to do anything that is not in the interest of our people and this administration.
"I am calling on my colleagues in the Senate and House of Representatives to come back and consider the requests of Mr President for the virement and supplementary budget for INEC for the 2019 elections," he said.
The ruling APC, hit by a gale of defections and internal wrangling in recent weeks is presently fighting a tough political battle, even as it prepares to retain power in 2019 in the midst of a phalanx of opposition parties and coalitions.