Murdoch's powerful News Corp Australia newspapers, which have the largest circulation of any media group in the country, have already called for voters to "kick out" Rudd's centre-left Labor government.
But the Australian-born octogenarian went further Tuesday, talking about the character of the two men who are facing off in the September 7 polls.
"Conviction politicians hard to find anywhere," Murdoch tweeted.
"Australia's Tony Abbott rare exception. Opponent Rudd all over the place convincing nobody."
Rudd's daughter Jessica Rudd, a writer, was quick to respond, tweeting back: "@rupertmurdoch Thanks for taking the time each day to tell us what to think."
News Corp has made no secret of its support for Abbott, with Sydney's Daily Telegraph running a front page editorial the day after Rudd called the polls under the headline "Kick This Mob Out".
The tabloid has since run a string of stories against the government, including one in which Rudd was photoshopped to look like bumbling Colonel Klink from television show "Hogan's Heroes" wearing a Nazi uniform and monocle.
Although now a US citizen, Murdoch's support is seen as influential in Australian politics and Rudd, who received the powerful tycoon's backing ahead of the 2007 election which he won, has accused the mogul of an orchestrated plan against him.
"Mr Murdoch has said in black and white that he wants Mr Abbott to be prime minister of Australia, (and) no one disputes he controls 70 percent of newspapers," Rudd said earlier this month.
News editors had been told to "Go hard on Rudd, start from Sunday and don't back off", Rudd added.
Murdoch has been a critic of Labor's plan for a multi-billion-dollar National Broadband Network (NBN) and also fiercely opposes proposed media reforms, which were set to include a new public interest test for major mergers and stronger self-regulation requirements
Rudd has suggested Murdoch is using his newspapers to attack Labor because he sees the party's NBN as a threat to the business model of its part-owned Foxtel cable TV company.