Parliament's Culture, Media and Sport (CMS)Committee has said on Friday it would be writing to Murdoch asking him for more details about evidence he gave earlier this month about phone-hacking allegations at the News of the World tabloid that has shaken his father Rupert's media empire.
The two Murdochs along with former News International chief executive Rebekah Brooks appeared before the committee on July 19 when they were pressed about phone-hacking and payments to police by News of the World reporters.
"We are going to write to ask for further details on areas where evidence is disputed," said the committee's chairman John Whittingdale.
While the committee voted against immediately recalling Murdoch, chairman of British newspaper arm News International, Whittingdale said it was likely he would be recalled at a later date over claims some of his original testimony was wrong.
Tom Crone, News International's former top legal officer, and Colin Myler, editor of the News of the World until it was shut down earlier this month, have disputed some of James Murdoch's evidence.
Murdoch said he had not been in possession of all the facts when he approved a large payout to English soccer executive Gordon Taylor, one of the phone-hacking victims.
But in a statement, Myler and Crone said they had told him of an email from a News of the World reporter to "Neville," containing transcripts of hacked voicemails. Neville Thurlbeck was the paper's chief reporter when it published a story about Taylor.
Whittingdale said the statement had "raised questions over some of the evidence that we have received" and they would also be contacting Crone and Myler.