The board of the FAI has expressed its "deep disappointment" with comments made at today's Oireachtas Sports Committee meeting.
Minister for Sport Shane Ross was before the Committee to discuss the association's finances.
The FAI, whose liabilities stand at over €55 million, were not at the meeting.
Minister Ross revealed that the FAI sought an €18 million bailout from the government on Monday of this week.
He described this was "shocking", saying the association sought either the funding or "alternatively a guarantee" of that figure.
He also confirmed that "not one euro" of a new funding scheme for youth football and grassroots development officers will go to the FAI.
Following the meeting, Minister Ross and Minister of State with Special Responsibility for Tourism and Sport Brendan Griffin sought to clarify matters around the League of Ireland.
It came after comments made by Sinn Féin TD Jonathan O'Brien at the meeting who said that "if the FAI goes, the League of Ireland goes the same way".
'Urgency' over LOI future
The Ministers said they were "enormously concerned" about the future of the League.
They said in a statement that "that the insolvency of a national football federation in Europe would be an unprecedented situation and thus it is not completely clear what implications this would have for the relevant national league and consequently international teams".
Their understanding is that the league "would cease to exist in its current format" in the event of the failure of the national association.
They said that "we understand that League of Ireland clubs would be in a position to rebound quickly and fulfil fixtures if such a failure were to occur in the FAI".
They added: "In that case, it would avoid a scenario where national teams would be precluded from international competition, provided a replacement national federation would be in place."
The Ministers said they would seek clarification from UEFA ahead of their meeting next month and to have "certainty around this point as a matter of urgency".
FAI had presented 'credible business plan'
The board of the FAI responded by saying statements made at today's Committee meeting made its efforts to secure the association's financial future "more difficult".
In reference to Minister Ross' admission about an €18 million bailout, they said confidentiality had been broken.
FAI Executive Lead Paul Cooke said some of the points raised today were discussed in confidence at Monday night’s meeting, where they presented the government "with a credible business plan".
He said: “The Board, management and staff at the FAI are working hard to avoid an insolvency process.
"We know better than anyone the consequences that would have on our international teams, the League of Ireland and the hundreds of thousands who play football up and down the country every weekend.
He said they were "frustrated" at the delay in the appointment of an Independent Chairperson and three Independent Directors.
Mr Cooke said: “Until the refinancing package is signed-off, it is unlikely that Independent Directors will be available for appointment.
"What was said in the Oireachtas today will not help the recruitment process for those Independent Directors.
“The purpose of the meeting with Government on Monday was to expedite the completion of the refinancing deal, thus allowing the nominated Independent Directors to complete their own due diligence and take up their roles. That remains the priority of the Board.”
'Serious concern' over jobs
Meanwhile, a delegation from the trade union SIPTU also met with Minister Ross this evening to discuss the future of those employed by the FAI.
They relayed concerns from staff and those involved in grassroots football across the country and said that morale "is at an all-time low".
SIPTU Sector Organiser Denis Hynes said that Minister Ross agreed that there "is a serious concern in the FAI over job security and its future financial viability".