Cotton was quoted as saying "unofficial meetings are taking place" about England and France pulling out of the Five Nations and creating a new tournament in which they would be joined by Australia, New Zealand and South Africa.
Richardson said Cotton's reported comments "defy belief and leave us to query his motives. We have never expressed any wish to withdraw from the Five Nations."
Cotton was quoted in the Daily Mail as saying some people, mostly on the RFU executive committee, want England out of the Five Nations. "They have got to be stopped. They think England's best interests are served by not being part of the Five Nations, that they'd be better served with the southern hemisphere countries." He added: "I will fight this tooth and nail."
Richardson dismissed Cotton's comments. After stressing England's commitment to the tournament, he added: "Indeed, only last September it cost us considerable money to settle with the other countries regarding TV rights in order to stay in. We have always said that the Five Nations is vital to us."
In their statement, the RFU countered claims by Cotton that the RFU's AGM had been misled over several aspects of Sky's television contract. He rejected Cotton's suggestions that the RFU did not have a veto on Sky showing Five Nations games on a pay per view basis and that the RFU did not have control over match scheduling. The timing of other England matches, the RFU said, would be a matter for agreement by all involved parties.
The RFU also said Sky could not, as Cotton suggested, dictate the structure of the domestic rugby. The RFU said: "In return for their investment, BSkyB reasonably wish to be advised and consulted over any changes to the format." A reduction in the size of the First Division, for example, would influence Sky's match coverage.
"BSkyB's ability to influence the decisions of the RFU is no lesser or greater than the BBC has had for many years. The AGM was not misled," the statement concluded.
As they seek to defend the World Cup Sevens in Hong Kong, England contain five of the side that took the inaugural World Cup crown at Murrayfield, including Tim Rodber, who has taken over as captain following the withdrawal of Lawrence Dallaglio. England begin their defence against Canada and Zimbabwe on Friday.
Wales, weakened by late injuries to Neil Jenkins and Robert Howley, face Namibia and then the formidable Western Samoans. No fewer than seven of the original squad of 10 players were forced to withdraw and the coach, Kevin Bowring, now has a party that includes six uncapped players.Reuse content