The Dragons, Ospreys, Scarlets and Blues have issued a joint statement in response to criticism from Welsh Rugby Union boss Roger Lewis.
Talks over compensation to the regions for their players' absence on Wales World Cup duty broke down last week.
Lewis expressed disapproval of the fact that the problems had been made public and said there was a threat that the regions would keep players from Wales.
The regions dispute this and call Lewis' comments "highly inaccurate".
At no time have the regions threatened the withdrawal of players from this year's Rugby World Cup
Statement from the Welsh regions
Lewis said he was disappointed that details of private discussions had been leaked by the regions to the media, but they say that they were not to blame and have urged the WRU to look at their own organisation.
"At no time have the regions threatened, or even intimated, for any reason, the withdrawal of players from this year's Rugby World Cup - nor would such action be considered," says their statement.
"At no time until Roger's statement were the regions aware of any fundamental disagreement in the combined efforts of the regions and the WRU to arrive at a new participation agreement.
"The regions have enjoyed a strong working relationship with the WRU, where ideas for the betterment of the game and its governance have been generated in an atmosphere of mutual co-operation and respect.
The WRU is saying a firm and decisive 'no' to this demand
"We remain deeply committed to the game in Wales and to the success of the Welsh team."
WRU group chief executive Lewis has issued a counter-statement disputing the regions' claim that they were unaware of problems in the participation agreement and expressing his "disappointment" at what he sees as a personal attack.
"It is time for these discussions to move back into the meeting room, not in the press, and I look forward to meeting the regional representatives once more later this month," he said.
The regions were seeking £30,000 per man as compensation for World Cup absences, a figure that would cost the WRU close to £1m.
But the governing body maintains that the substantial increase in central funding received by the four regions covers the release of players for international tournaments.
The sum the four regions get from the Union has risen from a combined £1.8m to £3.4m for three years until 2009.
The WRU said that the regions have not made similar applications for compensation from the Ireland and Scotland unions.
They also noted that English Premiership clubs Gloucester and Worcester, who provide two members of the Wales World Cup squad, have not applied for compensation.
Lewis said last week: "We are saddened that on the eve of the Rugby World Cup, the four regions have adopted this approach and have put unnecessary pressure on Wales' build-up."
The players selected for the World Cup will definitely be unavailable to the regions for at least two months, possibly increasing to three months if Wales make it through the group stages and into the knock-out rounds.
The Ospreys, Blues, Dragons and Scarlets were also seeking recompense for all the preparation time their star players have spent with the Wales squad.
English clubs have agreed a £30,000 per man compensation deal with the Rugby Football Union for the loss of their players during the World Cup.
"The incredible disappointment we feel over the attitude and actions of the four regions is tempered by our determination to stand firm on this issue for the sake of Welsh rugby," said Lewis last week.
"The four regions have been demanding nearly £1m in compensation for releasing their players to pull on the red jersey of Wales in the greatest rugby tournament in the world.
"The WRU is saying a firm and decisive 'no' to this demand because it would not be fair to the rest of Welsh rugby."