The IRFU, The Welsh Rubgy Union and the Scottish Rugby Union say they will not sanction any of its regions or clubs playing in future tournaments they do not fully approve of.
It follows plans announced earlier this week for a new Rugby Champions Cup next season led by top English and French clubs.
Premiership Rugby and Ligue Nationale de Rugby say they have no interest in resuming negotiations with European Rugby Cup over a new tournament agreement for the Heineken Cup and Amlin Challenge Cup competitions. The current accord expires next summer.
Talks are not planned to resume untiil October 23, and ERC has appointed a mediator - Canadian lawyer Graeme Mew - in an attempt to bring all sides together.
But Premiership Rugby and LNR are forging ahead with their own plans, having also extended an invitation to Celtic and Italian teams to join them.
"The Irish Rugby Football Union wishes to clarify that its clubs/provinces will not be participating in future tournaments which do not have the full approval of the International Rugby Board (IRB) or the relevant National Rugby Unions," the statement read
"The IRFU and its clubs remain fully committed to the development of a pan European Rugby Competition and we welcome the recent comments made by the IRB Chairman, who confirmed that a pan European tournament remains the goal of the IRB.
"We are confident this can be achieved.
"Our focus now is to work collaboratively with our colleagues across Europe, encouraging all parties to come to the table in order to engage in and conclude negotiations as speedily as possible."
Similar statements from the Welsh Rugby Union and Scottish Rugby Union were released on twitter almost simultaneously.
The French Rugby Federation, meanwhile, has already said they will not support any new Anglo-French
Premiership Rugby and LNR, though, plan to finalise structural detail of the Rugby Champions Cup when it knows who will be involved.
Speaking earlier this week, Premiership Rugby chief executive Mark McCafferty said: "Before we can release more information we need to know over the next few weeks which other teams will be joining the competition.
"Once we know the final, or close to final, numbers then we'll settle on the competition formats.
"Various people have approached us about the possibility of joining and we've indicated to them that we'll keep their names confidential.
"We've heard that other people want to be involved in European competitions, that's why we've left the door open and expect it to be more than an Anglo-French competition.
"We're asking for the RFU's (Rugby Football Union's) support against the background that there will be no ERC competition in which we're taking part at the end of the season. We need to put in place new competitions."
The news comes after Bruce Craig, the owner of Bath, said the existing European competitions were “finished” and that the only way forward for Celtic League sides was to join the Anglo-French inspired Rugby Champions Cup, which was launched on Sunday.
“If the competition is not approved then that would have absolutely catastrophic implications for Celtic rugby,” Craig told BBC Radio 5 Live. “The Heineken Cup is finished, it’s over. The Rugby Champions Cup is a way to save European rugby.
“The amount of money that is generated in the English and French games through our domestic leagues accounts for approximately 80 per cent of our revenues, so the implication of not playing in a Heineken Cup is much less serious for French and English clubs than it is for the Celtic nations.
“People say the English and French clubs are greedy. The fact is we are losing money.”
Craig confirmed English and French clubs would boycott the next ERC stakeholder meeting in Dublin on Oct 23.
“The reality of it is that if the Rugby Champions Cup doesn’t happen, then the Celts will not be playing in a competition and they won’t have those distributions from that competition.
“This new competition is one in which all the clubs are invited to play and there will be an equal distribution of money on a per-team basis.
“The unions should be approving that so there is continuity in English, French and Celtic rugby, because if there isn’t, there would be financial oblivion for the Celtic countries.”