FIFA rejected Ireland's request to replay its World Cup qualifier against France on Friday, while Thierry Henry said a rematch would be "the fairest solution" to resolve the furor over his extra-time hand ball that set up the deciding goal.
Turning down an appeal by the Football Association of Ireland as well as pressure from lawmakers in both countries, FIFA said it could not interfere and the referee's decision to allow the goal stands.
"The result of the match cannot be changed and the match cannot be replayed," FIFA said in a statement. "As is clearly mentioned in the laws of the game, during matches, decisions are taken by the referee and these decisions are final."
Henry used his left hand to keep the ball from going out of play, then passed to William Gallas, who headed in the decisive goal.
At the time of Henry's handball, which went unpunished by Swedish referee Martin Hansson despite fervent appeals by Ireland players, the match was 17 minutes from reaching a penalty shootout.
The 1-1 draw at Stade de France put the French through to next year's World Cup in South Africa 2-1 on aggregate.
Henry was jubilant in his goal celebrations but more subdued at the end of the match and admitted to handling the ball.
The France captain said after the game that the referee was at fault for not spotting the offence but waited until after FIFA's ruling to acknowledge the possibility of a replay.
"Of course the fairest solution would be to replay the game, but it is not in my control," Henry said in a statement issued to the media.
"Naturally, I feel embarrassed at the way that we won and feel extremely sorry for the Irish, who definitely deserve to be in South Africa.
"There is little more I can do apart from admit that the ball had contact with my hand leading up to our equalizing goal and I feel very sorry for the Irish."
Henry again denied deliberately handling the ball, although television replays suggested he slapped the ball once to stop it going out of play and again to set up the pass to Gallas.
The 1998 world champions won the first leg of the playoff in Dublin 1-0, but only scored with the aid of a huge deflection off an Ireland defender.
Ireland captain Robbie Keane suggested the French Football Federation act upon Henry's statement and ask FIFA to grant a replay.
"To make such a statement took courage and honour, and all of us recognize that," Keane said. "I would also be happy for a replay to happen in the interest of fair play so that whichever team qualifies can do so with their heads held high."
In Dublin on Friday, the FAI said it had received FIFA's reply rejecting a replay. The FAI said its management board would meet to consider the matter later Friday.
Irish Prime Minister Brian Cowen raised the issue Thursday with French President Nicolas Sarkozy at a meeting of the 27 EU leaders in Brussels.
FIFA did order Uzbekistan and Bahrain to replay a World Cup qualifying match in 2005 following a referee's critical error. However, there is no precedent to order a replay because of second-guessing a referee's judgment on the field of play.
Irish lawmaker Joe McHugh said France should follow the 1999 precedent set by Arsenal manager Arsene Wenger, a Frenchman who volunteered to replay a match in England's FA Cup after the Gunners won on an unfair goal.
Wenger backed calls to replay the match.
"I like justice in sport," Wenger said. "There are only two opportunities: One is France can offer to replay, which I support personally; the second is that FIFA has to make a decision on that issue."
Many in France, including political leaders, have urged FIFA to approve a replay.
François Bayrou, the leader of political party Modem, said the match should be replayed. Finance Minister Christine Lagarde said she felt "very sad" that the national team had qualified for the World Cup by "cheating."