The leading French clubs will not play in the Heineken Cup next season even if they are prevented from taking part in the new cross-border tournament they are setting up with Premiership Rugby.

The French Rugby Federation issued a statement hours after the French and English clubs – who gave notice in June last year that they were withdrawing at the end of the season from the two competitions run by European Rugby Cup Ltd – announced they were setting up the Rugby Champions Cup and would be inviting sides from the three Celtic countries and Italy to join, saying it would not give permission for the Top 14 sides to play in a new cross-border tournament.

It told them to take part in the mediation process ERC has started in an attempt to resolve a dispute which has centred essentially on control. The clubs feel they should run tournaments they are involved in, something the Celtic unions and Italy, who hold the balance of power on ERC, vehemently disagree with.

"The RFU has a similar position regarding Premiership Rugby that the FFR does with its clubs," said the chairman of ERC, Jean-Pierre Lux, at the launch of this season's Heineken Cup in Paris on Monday, pointing out that clubs were not allowed to take part in cross-border tournaments without the consent of their unions.

"The recent media release from the Ligue Nationale de Rugby and Premiership Rugby lacked respect," Lux continued. "The impasse is essentially because Premiership Rugby want to renege on a binding commercial deal in favour of their questionable TV contract with BT. I sincerely hope that people reflect on their current problems and I hope we will be able to reach an agreement when we have another opportunity to engage on 23 and 24 October with the mediator Graeme Mew."

Saracens chief executive Edward Griffiths believes it is only a matter of time before club competitions are run by the clubs. Photograph: Christopher Lee/Getty Images

The French clubs are adamant they will not be involved with ERC next season even if they are prevented from playing in the Rugby Champions Cup. The stance of Premiership Rugby, which contrary to Lux's claim has not been told by the RFU that it has agreed to back the FFR and black the new tournament, is the same and it has pointed out that the binding commercial deal referred to by Lux, the extended television contract deal with Sky, was signed after the English and French clubs had given their notice to pull out and was therefore not binding on them.

"If the International Rugby Board or the unions try to stop the Rugby Champions Cup, two things will happen," said the Saracens chief executive, Edward Griffiths in Abu Dhabi on Monday. "First, it is almost inconceivable that a governing body of a sport would prevent a competition taking place which brings £60-70m into the game. Second, if they did try to stop that, there would be no European rugby.

"The English and French clubs have been very clear they are not going to go back to an ERC tournament: no European rugby at all would obviously not suit anybody. If you look at the history of professional rugby, it has always been about this balance between union control and the clubs. That has been a fraught balance at times.

"The BT Sport television deal has given the English clubs more of a chance to redress that imbalance. The unions should run the national team and some of the grassroots and the clubs should run the club game. That is what happens in most mature professional sports. I think it is just a matter of time before that happens in rugby."