The Football Association of Ireland has issued a statement saying that the suggestion of an additional place at the World Cup is "not a possibility" and that the matter was "peripheral".
FIFA president Sepp Blatter this week revealed that the Republic were bidding to be installed as a 33rd team at the World Cup.
The FAI has said that it was "not raised in any of its formal written submissions to FIFA" and has requested that it will not be raised at today’s FIFA Executive Committee meeting.
Republic of Ireland assistant manager Liam Brady claimed the FAI, having already had calls for a replay rejected, had expected FIFA to consider the '33rd team' request in private, rather than go public with it.
The FAI today said the proposal was explored "only fleetingly as part of a wide-ranging 90-minute discussion" with FIFA.
"Regrettably the matter appears to have been singled out in public by Mr Blatter despite his assurances that the meeting would remain private."
Brady had yesterday expressed dismay at the way Blatter has dealt with the saga since Giovanni Trapattoni's side were cruelly knocked out.
"He's a bit of a loose cannon. He's an embarrassment to FIFA," Brady said.
And today the FAI said that instead of diverting attention, "they would prefer that Mr Blatter uses this opportunity to deal with the issues which have been raised formally for the benefit of football worldwide."
The association then went on to list some of the issues for FIFA to look at such as video technology, goal-line assistant referees and stronger sanctions "for players involved in match-defining breaches of the laws of the game".
Ireland were beaten by France in the second play-off by a goal which should have been disallowed due to Thierry Henry's handball.
They also wanted FIFA to ensure that their "rules cannot be changed mid-way through a tournament, for whatever reason, commercial or otherwise".
This was in reference to the fact that seedings were brought in by FIFA at the draw for the World Cup play-offs which ensured that the top countries avoided each other in the play-offs.
The FAI also called on FIFA to issue a clear statement that they do not condone breaches of the laws of the game.
They said: "For a man in Mr Blatter’s position to empathise with someone who scored a goal by cheating is inappropriate."