Gbajabiamila was endorsed by the party at a meeting hosted by President Muhammadu Buhari on Tuesday night.
A member John Dyegh (Benue) said the North Central caucus was not satisfied with the decision.
He said the North Central caucus has asked the leadership of the All Progressives Congress (APC) to reconsider the decision and zone the seat to the North Central.
It would be recalled that Chike Oakford (Imo) also declared his intention to run for the Speaker’s office on Tuesday shortly before the Presidential dinner, saying that the Southeast deserved the Speaker’s position for the 9th House of Representatives.
Okafor said the party must look beyond numbers but more on fairness and equity.
Dyegh told reporters the loyalty of the North Central caucus to the party, went ahead to declare his intention to vie for the position of the 9th Speaker of the House.
“We are not fighting the party, we are not. We shall not, we are only giving the party an opportunity to come back and look at the zoning and look at what we are saying.
“Taking what the party says hook, line and sinker is not democratic, we are in a democracy. We have right to vie for position, there’s freedom of expression.
“We believe in party supremacy. Yes, the party is supreme. I sing that, I say it, I believe it, I go by what the party says but this is democracy and I believe we should give the Green chamber an option.”
According to him, in addition to being the third largest contributor to the 2019 election success of the party, fairness and equity demands the North Central be considered for the position since the region has never produced the Speaker or Deputy Speaker since the return to democracy in 1999.
He said: “My party the APC in her wisdom zoned the position of Speaker to the South West and even micro-zoned.
“I am a party man and my loyalty to the APC is 100 percent, however, the North Central zone has not been convinced nor given reasons why their votes should not count and why we should not run and we feel very strongly that there is still room for negotiation because we believe “it is not over until it is over’.
“We are therefore appealing to the party to have a rethink and rezone the speakership to the North Central for justice and fair play. We pray to God Almighty to touch the hearts of our Leaders to reconsider us favourably.”
On his candidacy for the post, the lawmaker said the decision to join the race was based on his unyielding faith in a united and prosperous Nigeria.
Citing sections of the constitution, Dyegh noted: “It will only be fair, if the position of Speaker is given to the North Central, having taken away the seat of Senate President to the North East.
“It is instructive to note that the North Central has neither produced Speaker nor the Deputy Speaker since 1999.
“We are saying that reward in politics is based on what you bring to the table and the North Central brought the third highest number of votes in making President Muhammadu Buhari’s second term a reality and enabling the APC to form Federal Government”.
On his agenda if successful, Dyegh said the Independent National Electoral Commission (INEC) would be re-organised while the Electoral laws would be reviewed for enduring electoral processes.