British Prime Minister David Cameron says News Corporation executive James Murdoch has “questions to answer” about disputed testimony he gave to Parliament this week about how much he knew about the phone-hacking scandal engulfing his company.

Murdoch, the heir apparent to Rupert Murdoch's vast global media empire, told a parliamentary investigative committee that when he authorized a $1.1 million payment in 2008 to one victim of phone-hacking by a reporter at the now-closed News of the World tabloid he was not aware that the interception of voicemails went beyond the activities of one rogue journalist.

But British lawmakers on Friday demanded new answers from the 38-year-old Murdoch after two former executives at the media company disputed his account. A former editor at the tabloid, Colin Myler, and Tom Crone, the former legal adviser at News International, the Murdochs' British subsidiary, both said he was “mistaken” about not knowing about the extent of the phone-hacking.

Myler and Crone said that as Murdoch moved to settle the lawsuit by approving the unusually large payment to soccer union leader Gordon Taylor, they informed him of a crucial email containing the transcript of a hacked cellphone message that was marked to be sent to a key reporter at the newspaper.

Murdoch said he stands by his testimony. But Mr. Cameron said that “clearly James Murdoch has got questions to answer in Parliament” and that News International has “a mess to clean up.”

The latest dispute over the phone-hacking at the tabloid that the Murdochs closed two weeks ago came as there were new allegations that reporters at the newspaper paid London police about $500 for each time they wanted to locate people by tracking their cellphone signals. It is a practice known as “pinging,” for the way cellphone calls bounce off of relay towers.