First Minister Arlene Foster has refused to call for UDA boss Dee Stitt to quit his role as chief executive of Charter NI.
The DUP leader was opening an extension to the community facility Fermanagh House on Thursday morning in Enniskillen.
It has received £920,000 worth of funding from the Executive's Social Investment Fund - the same scheme which gave £1.7million to Charter NI to which Mrs Foster was pictured at the award announcement.
Asked by the BBC if she would call for Stitt to reconsider his position as chief executive, as deputy First Minister Martin McGuinness has, the MLA said it was not for her to advise the organisation on employment issues and to "sack" its chief executive.
She said that the attention on the loyalist had become a distraction to the work of Charter NI.
When pressed if, as Martin McGuinness said, Stitt should himself reconsider his position, the first minister responded: "He had his position and she had hers".
Since the awarding of funding to Charter NI and an interview with The Guardian - in which Stitt said the Government didn't care about Northern Ireland - he has faced mounting pressure to stand down as the ex-prisoners' organisation boss.
He apologised to the board of Charter NI and it issued a final written warning following an internal review.