Former prime minister Malcolm Turnbull says his predecessor Kevin Rudd is peddling an "insane conspiracy theory" that he conspired with Rupert Murdoch to undermine the National Broadband Network for News Corporation's benefit.

In an opinion piece for The Sydney Morning Herald and The Age last week, Mr Rudd accused Mr Murdoch of "getting [former prime minister Tony] Abbott and his then communications minister Turnbull to destroy my government’s Fibre Optic to the Premises National Broadband Network", and called for a royal commission.

Former prime ministers Kevin Rudd and Malcolm Turnbull are at loggerheads over News Corp's involvement in "destroying" the NBN. Credit:Alex Ellinghausen

In discussions with Reddit users this week, Mr Rudd accused the ABC of failing to hold Mr Murdoch to account over his "vicious pursuit of his commercial interests, as seen in his determination to destroy the NBN".

Former ABC journalist Quentin Dempster asked Mr Turnbull's son Alex about the issue over Twitter on Friday, prompting the senior Turnbull to intervene.