Fifa has ruled out any prospect of France and the Republic of Ireland replaying their World Cup play-off match, despite the Irish justice minister, Dermot Ahern, this morning joining the Republic of Ireland assistant manager, Liam Brady, in calling for a rematch.

When contacted by the Guardian, a Fifa spokesman flatly denied the chance of a rematch, refering to Law 5 in the official rules of the game, which states that the referee has "full authority to enforce the Laws of the Game in connection with the match to which he has been appointed", and that "the decisions of the referee regarding facts connected with play are final".

In case there was any question whether this leaves room for doubt, the International FA Board notes that: "Facts connected with play shall include whether a goal is scored or not and the result of the match." The fourth assistant at the match, Martin Ingvarsson refused to be drawn today when questioned about the incident. "We are not allowed to make any comments at all in connection to Fifa games," he said.

Ahern was dismissive of what he perceives as Fifa's lack of leadership and moral courage following the Thierry Henry handball which led to William Gallas's extra-time equaliser. "Millions of people worldwide saw it was a blatant double handball – not to mention a double offside," Ahern said. "We should put the powers that be in the cosy world of Fifa on the spot and demand a replay.

"They probably won't grant it as we are minnows in world football but let's put them on the spot," Ahern added, indicating that despite Fifa's stance there may yet be an official complaint. The minister is thought to have asked the Football Association of Ireland chief executive, John Delaney, and the vice-president, Des Casey, to demand Fifa arrange a replay.

"It's the least we owe the thousands of devastated young fans around the country. Otherwise, if that result remains, it reinforces the view that if you cheat you will win. Thierry Henry has admitted handling the ball, claims he told the ref he handled it," Ahern added.

Brady was also scathing of Fifa. "For the dignity and integrity of football, we will go to France and play again," he said. "[The Fifa president] Sepp Blatter goes on about fair play – let him reflect on what happened last night. Where is football going if a team is cheated out of fair play? Where are we going if this decision stands?"