Premiership Rugby and its French counterparts have been accused of showing a lack of respect during an increasingly bitter row over the Heineken Cup's future.
Top English and French clubs have announced plans for a new tournament next season, the Rugby Champions' Cup.
And Premiership Rugby chief executive Mark McCafferty has said that he expects Celtic and Italian teams to join them.
The French Rugby Federation, though, indicated it would not support such a venture. Any Anglo-French breakaway tournament would require FFR and Rugby Football Union approval as respective governing bodies.
Canadian lawyer Graeme Mew has been brought by European Rugby Cup to act as an independent mediator in the dispute. The next round of negotiations is planned for October 23.
But Premiership Rugby and LNR currently have no intention of being involved after failing to make headway with ERC over financial, qualification and competition structure changes that they want to the Heineken Cup and Amlin Challenge Cup.
The existing tournament accord expires next summer. English and French clubs served notice to quit the current agreement last year.
But speaking at Monday's Paris launch of this season's Heineken and Amlin competitions, ERC chairman Jean-Pierre Lux was in a combative mood.
"The FFR has now officially reminded the LNR that no international game involving French clubs can take place without the advance permission of the FFR. And the RFU has a similar position regarding Premiership Rugby," Lux said.
"The recent media releases from the LNR and Premiership Rugby lacked respect.
"In June, the LNR committed to the principle of central marketing for ERC's tournaments which has been the at the heart of European club rugby's commercial success.
"While this process began in 2012, ERC met with the parties during the summer, with the exception of Premiership Rugby, who refused to engage. They have never entered into negotiations.
"This impasse is essentially because Premiership Rugby want to renege on a binding commercial deal in favour of their questionable TV contract with BT (Sport).
"I sincerely hope that people reflect on the current problems. We have another opportunity for everyone to finally engage with the process with the meeting on October 23 and 24 with the International Rugby Board-recommended mediator, Graeme Mew.
"I hope we will be able to reach an agreement. It would be disastrous to deprive so many players and fans of the opportunity of participating in such an outstanding tournament."
McCafferty has said a new competition would be overseen by an "organising body of some sort - it doesn't need to be as big, unwieldy or institutionalised as ERC".
And he denied ERC claims that the detail of its TV deal with BT Sport is shrouded in mystery - "the RFU know what's in it," he said - while adding that the French clubs will only play in a competition involving their English counterparts.
Ireland star Paul O'Connell, who helped Munster lift the Heineken Cup on two occasions, has expressed his hope that the situation can be resolved.
"It is obviously a big concern," said former British and Irish Lions captain O'Connell, who was speaking during an Ireland squad training camp directed by new national coach Joe Schmidt.
"There are administrators working on it at the moment, and hopefully they are trying to save the competition in some shape or form.
"You have just got to hope that the right people make the right decisions and it is beneficial for everyone in European rugby.
"It is very hard to speculate about what is going to happen."