The world governing body ruled that the result cannot be changed and the match cannot be replayed.

FIFA said in a statement: "FIFA has today 20 November 2009 replied to the request made by the Football Association of Ireland (FAI) to replay the 2010 FIFA World Cup play-off match held on 18 November 2009 between France and the Republic of Ireland in Paris.

"In the reply, FIFA states that the result of the match cannot be changed and the match cannot be replayed. As is clearly mentioned in the Laws of the Game, during matches, decisions are taken by the referee and these decisions are final."

The Football Association of Ireland (FAI) had formally requested a replay after Thierry Henry's clear handball in the build-up to William Gallas' decisive goal.

The announcement was not a surprise - a senior source at the world governing body had said yesterday they would have no option but to reject the demand.

The FIFA source told Press Association Sport: "There is no way the game can replayed.

"To do so would cause absolute chaos for football. If it was replayed then every match in the future would also be subject to these calls for a replay any time a referee misses an incident.

"FIFA's rules are absolutely clear. Law 5 states that a referee's decision on points of fact are final. That is the end of it. You cannot replay the match on this basis.

"You have to have a rule that says the referee's judgement is always right."

The wording of Law 5 of the Laws of the Game states: "The decisions of the referee regarding facts connected with play, including whether or not a goal is scored and the result of the match, are final. The referee may only change a decision on realising that it is incorrect or, at his discretion, on the advice of an assistant referee or the fourth official, provided that he has not restarted play or terminated the match."

The FAI had claimed there was a precedent because FIFA ordered Uzbekistan to replay Bahrain in 2006 World Cup qualifier after the referee made a "technical error" after a penalty had been awarded.

However, in that instance, the referee was guilty of wrongly applying the rules rather than missing an offence - he awarded an indirect free-kick against Uzbekistan when one of their players encroached on the Bahrain penalty area as the Uzbeks successfully converted a penalty. The correct interpretation would have been to order the penalty to be retaken.

Henry's handball would almost certainly have been spotted by an the extra assistant referee behind each goal-line - the system that is the brainchild of UEFA president Michel Platini that is being trialled in this season's Europa League.

Former Republic of Ireland midfielder Ray Houghton admitted he did not expect FIFA to order a replay as they are governed by the rules but he appealed to the French Football Federation to play the Irish again.

"I really feel it is up to the French Football Federation," he told Sky Sports News.

"If they are unhappy with the way they have qualified then they should ask for a replay. You don't want people going to the World Cup on the back of conning the referee or the officials.

"Surely for the sake of fair play, it should be replayed."

And Houghton called for FIFA president Sepp Blatter to make a public statement on the decision by football's world governing body.

"Where is Sepp Blatter? Why hasn't he come out and stood up and told everyone how it is.

"He's very good at telling other countries how to run their game. It really needed the top man to come out and tell the footballing public why they have made this decision."

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FIFA's response will now be considered by the FAI's board of management, which sits for a pre-arranged meeting this afternoon.

The FAI said in a statement: "Football Association of Ireland today confirmed that it has received correspondence from FIFA rejecting the Association's request for a replay of the World Cup play-off match between France and the Republic of Ireland.

"A previously scheduled meeting of the FAI board of management will take place this afternoon where the matter will be considered.

"No further comment will be made until this meeting has concluded."

mfl