The Greens, which hold the balance of power in the upper house, have called for a parliamentary inquiry into News Limited, Mr Murdoch's Australian firm.
Mr Murdoch appeared before a UK parliamentary committee on Tuesday.
"When people have seen telephones hacked into, when people have seen individuals grieving having to deal with all of this, then I do think that causes them to ask some questions here in our country," Ms Gillard told reporters in New South Wales.
"Obviously News Limited has got a responsibility to answer those questions when they're asked."
Australian journalists' unions said they backed the call by Greens party leader Bob Brown for an inquiry.
End Quote Julia Gillard Australian prime ministerObviously News Ltd has got a responsibility to answer those questions when they're asked”
The company dominates Australian media - it controls 70% of the newspaper readership and has extensive holdings in television, the internet, and other media.
The BBC's Nick Bryant in Sydney says that largely because News Limited owns most of the tabloid titles, the competition in Australia for stories and gossip is nowhere near as cut-throat or intense as that in Britain.
The tabloid agenda is also different, he says, without the same preoccupation with sex scandals and nowhere near the same salaciousness.
News Limited boss John Hartigan has launched a review of all payments made by the group in the last three years and has said he is willing to co-operate with any inquiry.
He has also denied allegations by governing Labor party members that News Limited has been running a campaign against them, describing his group's journalism as aggressive but fair.
The government has reportedly stalled a ruling by an independent panel in favour of Mr Murdoch's part-owned Sky News to run Australia's taxpayer-funded overseas TV service.
The panel had unanimously backed the Sky bid to run the Australia Network but the government imposed a "national interest" bar on the process.
News Corp has also been attempting a takeover of the Australian broadcaster Austar.