Mr Paul Azure Sampana, Chairman of Tema West Constituency of the party, issued the 24-hour ultimatum on Wednesday.
"If we don't receive a favourable response within 24 hours, we would organize and conduct our own primaries and introduce the winner to the party on July 13, at the party's rally at Kasoa".
He added that even though the NEC has planned to introduce all 230 parliamentary candidates of the party for the December election at the Kasoa rally, Tema West has nobody to represent them due to unnecessary delays of the primaries.
Mr Sampana alleged that the NEC was trying to suppress the will of the polling station chairpersons to hold the primaries, explaining that, with the exception of Tema West, primaries have been held in all the constituencies in the Greater Accra Region.
According to Mr Sampana, the NEC called him on telephone asking him to postpone the primaries which was scheduled for May 25, adding that the NEC has failed to communicate the date for the primaries or acclamation as promised.
He said even though the two aspirants, Mr Abraham Osei Aidoo, the incumbent Member of Parliament who has represented the constituency since 1996 and Mrs Irene Naa Torshie Addo, Deputy Ghana Ambassador to the United States passed the vetting, they do not understand why the hierarchy of the party were deliberately preventing the constituency from holding the primaries.
"It is in the interest of the party that primaries are held according to the party's constitution" noting that "it is unfortunate that people are interpreting the constitution to suite their own selfish interests, such people must know that the party is like a pyramid therefore they can't take decision for the constituency".
The Constituency Chairman promised that the constituency executive and the polling station chairpersons would leave the party should the NEC fail to give a date or accept the aspirant who would emerge winner, when the primaries is organized without their consent.
Mr Sampana lamented that while some party members have threatened to banish him from the constituency, some officials have also threatened to assault him should he step his foot at the party's office as they claimed he was delaying the primaries.