The media moguls have each given wide-ranging interviews over the weekend following a deadlock in negotiations between BSkyB and Virgin Media over carriage deal fees.
The spat means that the newly launched Virgin Media can no longer offer its customers Sky's basic channels and a number of first-run hit shows including 'Lost' and '24'.
Murdoch, the chief executive of BSkyB, has branded Virgin Media a company seeking "victimhood" in order to achieve its ends.
Murdoch also claims he was "astonished" by the government's recent decision to ask to launch a public interest probe through Ofcom into his acquisition of a stake in ITV.
The BSkyB chief executive warned Britain is in danger of allowing regulations to be "manipulated".
Virgin Media's refusal to accept the price being demanded by BSkyB to supply Sky channels to Virgin's cable service reflects a company unwilling to invest, Murdoch claims. Instead, Murdoch said Virgin was seeking victim status.
Commenting on the Ofcom investigation, recently ordered by Trade Secretary Alistair Darling, Murdoch said: "It means we, plus the other players in the market place plus the government, are going to have to spend a number of months spending money and enterprise dealing with an initial investigation. The sum total of squandered human enterprise from this sort of nonsense is astonishing."
Meanwhile, Branson accused BSkyB of trying to strangle Virgin Media from birth, but said the money saved from the company's refusal to strike a deal with BSkyB would be ploughed into its video-on-demand service.
He said: "The Virgin Central channel is a great channel, it has brilliant programming already... we are going to really push that channel and put any money that we will save from this into getting fantastic programming for that."
Branson also said the disagreement with BSkyB would form part of its submission to Ofcom in its investigation into Sky's 17.9% stake in ITV.
He said: "There must be a link. There are numerous other things that have gone on behind the scenes, which will all be submitted to the competition authorities.
"Just take Flextech [Virgin Media's content arm]: market share up but a unilateral decrease in the price, 'take it or leave it' - that can only be done when you are completely dominant. Yet their [Sky's] market share had dropped and they wanted a doubling of price, it's just too blatant for words."