Founder and Chairman of the Council of Elders of the National Democratic Congress (NDC),
Mr Portuphy was unable to attend because he has been hospitalised and Mr Mahama could not be reached, the statement said.
Mr Rawlings brought the General Secretary's attention to the serious complaints and petitions emanating from the elections and the potential damage to the party if no action is taken to rectify the wrongs.
"Mr Asiedu Nketia conceded that it was necessary to take due note of the several petitions and complaints by suspending or cancelling such elections so the allegations could be thoroughly investigated and elections re-conducted to instil sanity and confidence in the process," the statement said.
It added: "The General Secretary confirmed at the meeting that he had already directed some elections to be cancelled and re-conducted in some of the areas he had toured."
According to the statement, the ex-president, who governed Ghana between 1992 and 2001 has however learnt that the situation in Kpando in the Volta Region, for example, has deteriorated in spite of directives by the General Secretary.
"Elsewhere in some branches he has received complaints about constituency executives arriving with a list they read out as the branch executives, party registers not being used, candidates not being vetted, notice of polls in terms of venue, date and time not issued and executives not making nomination forms available to some potential candidates they do not approve. He also received reports of some branches where executives unilaterally decided that certain people were not members of the party," the statement noted.
It also quoted Mr Rawlings as saying: “I have observed that certain elements in the party who are supposed to be unbiased arbiters and supervisors in these elections are rather pursuing a parochial agenda that is not in the party’s interest. These limited victories are like winning a battle and losing the war. We witnessed this in the selection of our parliamentary candidates in the 2016 elections, which partly accounted for our humiliating defeat in that election.
"We are on the verge of breaking up the NDC if we pursue this path. The National Executive Committee has to take a serious look at the entire branch electoral process and ascertain whether they have been held in an open, free and fair manner devoid of foul play and deliberate abuse."
The former President urged all party members across the country who feel aggrieved by the conduct of the elections to forward their petitions and complaints to the party headquarters. Copies of such petitions can be sent to his office so the concerns can be pursued with the national executive, the statement concluded.