News Corporation, the media empire that owns The Sun and the Times titles, stands accused of running a secret unit to sabotage competitors, according to 14,000 emails released to the Australian Financial Review.
The Australian communications minister Stephen Conroy said the allegations should be referred to the Australian Federal Police for investigation.
He told his 207,894 followers of "Enemies many different agendas, but worst old toffs and right wingers who still want last century's status quo with their monoplies [sic]".
Mr Murdoch said on Twitter: "Let's have it on! Choice, freedom of thought and markets, individual personal responsibility."
The mogul, who has been on Twitter since New Year's Eve, has used the website to voice his opinions on a range of political and media issues.
Earlier this week, he criticised the British Prime Minister following an expose in the Sunday Times that revealed the Conservative party co-treasurer Peter Cruddas was offering access to David Cameron for "premier league" donors.
He said: "Of course there must be a full independent inquiry on both sides. In great detail, and with consequences. Trust must be established."
The latest claims against Mr Murdoch's company suggest NDS, a technology company that was part-owned by News Corp, had a secret unit which encouraged the widespread hacking of competitors.
The practice reportedly cost rivals $AUS50m (£33m) a year and helped put at least one out of business.
The Australian Financial Review made the claims this week, as it published thousands of emails from an archive held by Ray Adams, European chief of the unit called "Operational Security" between 1996 and 2002.
Pay-TV operators worldwide, including ITV Digital in the UK and Austar in Australia, were subject to a major wave of piracy during the period.
On Monday, a Panorama documentary on BBC1 alleged that NDS hired a man who ran a piracy website and tasked him with publishing "cheat" codes on the internet, allowing viewers to "crack" their ITV Digital boxes and use the services for free.
News Corp and NDS have vigorously denied the claims.