Jenny Palmer claimed she was put under pressure by Stephen Brimstone, who is originally from Kesh, to change a board vote in relation to the Red Sky maintenance company, a contract that was terminated in 2011 following claims of financial irregularities and substandard work.
Speaking to The Impartial Reporter, Ms Palmer, a Housing Executive board member, said: "I stand by every word I said because I told the truth."
The Lisburn councillor claimed in last week's programme that prior to the termination of the contract the brother-in-law of Enniskillen DUP Councillor Alison Brimstone telephoned her asking her to change her vote to terminate Red Sky's contract.
On BBC Spotlight, Ms Palmer recalled the conversation she had with Mr Brimstone two years ago: "He told me that he needed me to go against the decision of the board... I said I do not think I can do that. I went into shock. He said 'the party comes first. You do what you're told'. Otherwise there is no point in [you] being on the board, if I wasn't prepared to do what they asked me to do."
Ms Palmer says she stands by her claims and is considering accepting party leader Peter Robinson's invite to meet and discuss the allegations.
"Things are in a difficult place at the moment but I stand by every single word I said. It is the truth and in relation to meeting with Mr Robinson I am considering it," she told The Impartial Reporter.
She says she has been receiving support from across Northern Ireland from her party colleagues and added: "Obviously there is a restriction on terms of who can say what in the party. The support that my MP and Edwin Poots [DUP Health Minister] is giving me is helping me to keep my head up. Have I been tearful? Yes. I have absolutely nothing to hide; I know I am right; I know I am 100 per cent."
The Impartial Reporter attempted to contact Mr Brimstone in relation to the claims by Ms Palmer but was unsuccessful.
However, he did write to Spotlight last week to say he did not accept the accuracy of the account of events given in the programme.