Shortly after their first round of testimony before British Parliament in July, News Corp. CEO Rupert Murdoch and son James were already issuing revisions to what they'd told lawmakers about the company's hacking scandals.

After two former News Corp. employees pointed to inaccuracies in their testimony, James Murdoch admitted he was "mistaken" about payments made to an ostensibly "rogue" reporter who carried out illegal hacking operations. The backpedaling immediately prompted calls for him to return and testify again -- and this time, under oath.

Now that inquiry has officially called both men back to testify in October, and under different conditions.

In their next appearance, which Lord Justice Leveson wants televised, both men will be sworn-in and members of Parliament will be able to present evidence against the Murdochs, forcing them to respond. Witnesses may also be called, British media reported Wednesday.

If either is shown to have lied under oath, charges of perjury could be imposed.

Even without the oath, their prior session could have also ended with charges, although being accused of contempt of Parliament is incredibly rare.

Parliament's inquiry may ultimately take over a year to wrap-up.

A U.S.-based investigation is also under-way, probing whether News Corp. employees attempted to hack private messages meant for the victims of the attack of Sept. 11, 2001.