Murdoch took to Twitter to air his views after journalist Martin Hickman recommended that his followers read Neil's written statement to the Leveson inquiry into press ethics.
In a tweet yesterday (July 11) on @rupertmurdoch, the 81-year-old billionaire wrote: "@martin_hickman Anyone taking any notice of Andrew Neil on me is an idiot. Neil treated bestof all ex-employes now shows true colours (sic)."
Murdoch and Neil have had a frosty relationship ever since the latter man wrote Full Disclosure, an account of his time at the News International paper.
In his statement to the Leveson Inquiry, published yesterday, Neil appeared to contradict Murdoch's claim under oath to the inquiry in April that he had never asked a prime minister for anything.
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Neil said that Murdoch's "people" had lobbied the Labour Party to include measures ending the ban on foreign ownership of UK TV licences in the 2003 Communications Act.
This would, much later down the line, allow Murdoch's News Corporation to attempt to acquire the remaining 60.9% shares in Sky that it did not already own.
"This was something Mr Murdoch's people lobbied hard for, with his support, and they had unique and extensive access to the levers of power at the heart of the Blair government to make this lobbying effective," wrote Neil in his statement.
"When Mr Murdoch testified before this Inquiry that he had never asked government for anything it gave me cause to wonder if he had forgotten this - or forgotten he was testifying under oath."
But Neil, who was also previously the founding chairman of Sky, suggested that Murdoch and Blair had indeed reached an understanding ahead of the 1997 landslide victory for Labour.
"'How we treat Rupert Murdoch's media interest when in power', Mr Blair told me in 1996, a year before he became prime minister, 'will depend on how his newspapers treat the Labour Party in the run up to the election'. That is exactly how it panned out," said Neil.
"The Sun and the News of the World fell in line behind New Labour in the run up to the 1997 election, The Times stayed broadly neutral and The Sunday Times unenthusiastically Tory.
"After the election, The Times quickly fell in line as the New Labour house journal... in return New Labour in power did nothing to undermine or threaten Mr Murdoch's British media interests."