Negotiations over a new deal for the European Cup and Challenge competitions from the 2014/15 season will continue in Dublin later this month after a "comprehensive" meeting in Rome on Monday.
"ERC Accord discussions to continue in Dublin on 30 October after six hour comprehensive meeting in Rome today," tweeted competition organisers European Rugby Cup (ERC).
The English and French teams believe the European Cup's current format is weighted in favour of the Celtic nations, with Irish provinces Leinster and Munster having won five of the last seven editions between them.
Leinster have won three of the last four European Cups and their rivals in England and France claim that is partly a result of a qualification system that allows them to rest their players during the Celtic League season.
The English and French sides believe no more than six Celtic League teams should qualify, although that would put at risk the involvement of Scottish and Italian sides who currently qualify automatically.
The stakeholders in ERC are the respective national league authorities and federations from the Six Nations playing countries.
The meetings have come in the wake of an announcement last month by England's Premiership Rugby of a TV deal with BT Vision worth £152 million ($245 million) over four years from next season.
Continental rugby chiefs say a clause granting BT exclusive live broadcast rights to matches played by Premiership clubs in any future European competitions from 2014-15 for three years is invalid.
In a statement issued following a board meeting at its Dublin headquarters last month, ERC said the "purported deal" was in breach both of International Rugby Board (IRB) regulations and an ERC board mandate.
The statement said it was "unanimously agreed" at an ERC board meeting on June 6 that ERC would conclude a new four-year agreement with satellite broadcaster Sky Sports for the UK and Ireland exclusive live broadcast rights to the European Cup and the European Challenge Cup until 2018.
However, following that ERC statement BT's executive director Mark Watson said that he was willing to create a new European competition when the present deal with ERC ends at the climax of the 2013-14 season.