Craig's comments come after Rugby Football Union chief executive Ian Ritchie called on Friday for open-minded discussions "with a view to compromise on both sides".
Premiership Rugby and their French counterparts Ligue Nationale de Rugby served notice last year of their desire to quit the Heineken Cup and Amlin Challenge Cup when the existing tournament accord expires next summer.
They want changes to the structure of both continental competitions, principally over the number of teams involved, the qualifying process and how funds are distributed.
And disillusioned by what they view as a lack of progress during negotiations for a fresh competition agreement, they announced earlier this week plans for a new Anglo-French tournament next term.
Premiership Rugby met with Ritchie and other senior RFU figures on Wednesday night.
Any new competition would require approval from the RFU and French Rugby Federation as respective governing bodies.
Writing in the match programme for today's Bath versus Leicester Aviva Premiership clash, Craig said: "The game needs European rugby.
"There is no viable proposal made by any other party over the last 12 months of negotiation, and the Unions' position has become more entrenched for the status quo.
"The English and French clubs are taking the lead to save European rugby by proposing new competitions open to all existing participants.
"They are fair and meritocratic, and would certainly be in the public's interest.
"If the Unions in the coming weeks do not approve the competitions, through regulatory process, it will no doubt destroy European rugby and have catastrophic financial implications for Celtic and Italian rugby.
"The hour is grave, and I sincerely hope the English and French proposals are taken seriously and that we can all enjoy fabulous exciting European rugby in the future."
ERC chairman Jean-Pierre Lux and chief executive Derek McGrath confirmed on Friday plans for a mediator to be appointed as part of the negotiations aimed at thrashing out a new tournament agreement to take effect from mid-2014.
"Together, we confirm that it was agreed at last Wednesday's board meeting in Dublin, that ERC, as a signatory to the current accord, should be involved in all future negotiations aimed at the formulation of a new accord for the 2014-15 season and beyond," Lux and McGrath said in a joint statement.
"To that end, the board requested that ERC should convene the next, and future, meetings and that it should consider the appointment of a mediator to move the negotiations forward towards a successful resolution. This process is now under way.
"The board further agreed that bearing in mind the commitments the company has already entered into, no other structure other than ERC would be appropriate to organise European tournaments going forward.
"We believe it is now time for ERC's shareholders to cease public ultimatums and to enter into genuine and decisive negotiations aimed at strengthening European club rugby."