The Commons culture committee has recalled News International's chairman to give evidence. The company said Mr Murdoch would be "happy to appear". It comes after MPs heard conflicting evidence over how much Mr Murdoch knew about the practice at the NoW.
Separately, it has emerged the mother of a 7/7 bombing victim is to pursue a civil case against News International. The case of Sheila Henry, whose son, Christian Small, was killed in the 2005 Russell Square explosion, will be one of six test cases for civil damages claims against News Group Newspapers over phone-hacking claims.
'Happy to appear'
It is not known when Mr Murdoch will appear before the culture committee.
John Whittingdale, its chairman, said the committee wanted to first hear evidence from other witnesses, including former senior News Corporation executive Les Hinton and Mark Lewis, the lawyer representing alleged phone-hacking victims.
A spokesman for News Corp, the parent company of News International, said: "James Murdoch is happy to appear in front of the committee again to answer any further questions members might have."
Earlier this month, former NoW legal manager Tom Crone told MPs he was "certain" he told Mr Murdoch about an email which indicated phone hacking at the paper went beyond one rogue reporter.
Mr Crone said "it was the reason that we had to settle" a case. Former editor Colin Myler also told the committee the email was discussed.
Mr Murdoch, however, has insisted he was not told about the email.
In July, he and his father - Rupert Murdoch, head of News Corp - faced nearly three hours in front of the parliamentary committee, answering questions about what they had done to unravel the scandal at the News of the World.
At the High Court, Mr Justice Vos has been considering applications from a number of alleged phone-hacking victims to decide whose will be heard as test cases in the new year. Earlier, he added that of Sheila Henry to a list including actor Jude Law, MP Chris Bryant, interior designer Kelly Hoppen, sports agent Sky Andrew and ex-footballer Paul Gascoigne.
Other developments to emerge from the High Court hearing include:
- The family of murdered schoolgirl Milly Dowler, whose phone was allegedly hacked, have not issued proceedings.
- Lib Dem MP Simon Hughes issued proceedings against the NoW.
- Mr Justice Vos, himself, was told the Daily Star had linked him to hacking, but he said he had not been provided with any evidence. "I rarely leave or receive voicemail messages in any case," he told the court.
- New and significant information has been found at News International.