The FAI has issued documents which it says explain the "exact timelines" around the payment of €5 million by FIFA to the FAI in 2010 and revealed that an additional $400,000 was paid for "FAI Regional Centres".
In a lengthy document, the FAI outlines the process it says led to the payment of an "interest free" €5 million loan in January 2010 as compensation of the Thierry Henry incident that contributed to Ireland being eliminated from the play-off game against France.
The loan was subsequently written off by FIFA.
The FAI says the payment was made as compensation for reputational damage to the FAI after comments by Sepp Blatter disparaging Irish calls to be made a 33rd team at the 2010 World Cup.
Blatter publicly dismissed the idea when it was raised at a press conference in late 2009.
In the aftermath of Ireland's elimination by France in November 2009, the FAI says it requested that the match with France be replayed - an appeal that was turned down by FIFA.
The FAI says it then stated its intention to go to the Court of Arbitration for Sport.
The documents released tonight say that following this request, a meeting was held to resolve the matter at which Ireland's "potential recourse to legal action against FIFA" was discussed.
The FAI claims that at this first meeting it was agreed that neither party would discuss the matter in public.
However, the second meeting was called following Blatter's dismissive response to Irish calls to be the '33rd team'.
The FAI statement said this "was in direct breach of agreed confidentiality and subsequently brought reputational damage to the FAI".
At this meeting in Zurich, held in January 2010, the FAI says €5m was offered by FIFA. The FAI says an agreement was officially drawn up on 15 January.
The FAI says €5m was lodged into the FAI's National Irish Bank deposit account on 20 January, and first accounted for in the FAI's 2010 audited financial statements, under bank and other loans.
The FAI says the €5m was used to make payments to New Stadium Ltd - the trading name for Aviva Stadium management company - on 25 February and 26 March of 2010.
And according to the FAI documents, an additional $400,000 was also given by FIFA for "FAI Regional Football Centres".
According to the FAI, the figure for the loan was subsequently written down to €4m in 2011, and was reflected in the association’s turnover figure of €45m in that year's audited accounts.
The FAI says the loan was written down to zero in 2013 following Ireland’s failure to qualify for the World Cup in Brazil in 2014.
Speaking to RTÉ this evening, FAI Chief Executive John Delaney said he wanted "full disclosure" on the matter.
"I've heard a lot of talk over the last couple of days of letting the fans down. I was doing my best with the members of the FAI board to get us back with a sporting solution. It was only after the World Cup draw took place on 4 December with France in it that we then looked for a financial solution based on a legal case."
Delaney said a key issue for the FAI was the change in seeding procedure ahead of the play-off draw.
"It wasn't to be seeded, but Blatter, in that year, in September 2009, announced that it would be seeded. We felt that that changed the rules of the World Cup almost at the end of the tournament before we got our play-off, therefore we got France.
"The second thing is when he spoke on 30 November about our confidential meeting on 27 November he made a skit and that was a reputational damage. And he knew - and we knew - that that was of damage to the FAI.
"The handball was a catalyst for everything that happened afterwards."
Asked why the €5 million payment was not apparent in FAI records, Delaney said this was due to the confidentiality agreement that was "laid bare by FIFA".
"There is a fine in there of $250,000 if we spoke about it or disclosed the fact that we had got this money from FIFA.
"A year ago this appeared in the media and nobody paid much attention to it. I think it’s unfortunate that this story has got caught in all the other stories of FIFA. This was a good legitimate business deal for the FAI.
"We did very well out of it after we didn't get a sporting solution, we got a financial solution based on our legal case."