— Prime Minister David Cameron on Friday said James Murdoch, scion of media magnate Rupert Murdoch, should be recalled by Parliament to address allegations he misled lawmakers in his testimony on Britain’s phone hacking.

Further upping the pressure on James Murdoch, 38, an opposition lawmaker called for a police investigation into whether he lied.

At issue is whether News Corp. executives knew of the widespread practice of phone hacking at their now-defunct News of the World tabloid — which illegally accessed the phones of thousands of British citizens — and whether the executives tried to cover it up.

In another development, U.S. Justice Department prosecutors are preparing subpoenas as part of their inquiry into allegations that News Corp. employees sought to hack into the phones of victims of the Sept. 11, 2001, terrorist attacks and tried to bribe law enforcement officers for information, people familiar with the matter said Friday. The sources spoke on the condition of anonymity because the investigation is not public.

The subpoenas would seek information from the company related to the phone-hacking scandal that has engulfed Rupert Murdoch’s British media operations, the people said. Murdoch is chairman and chief executive of News Corp., which is based in New York and has extensive U.S. operations. James Murdoch heads up News International, the newspaper-publishing arm of News Corp.

It is unclear if or when subpoenas will be issued and specifically what information they would seek. The Wall Street Journal, which is owned by News Corp., first reported on the preparation of the subpoenas and said they still require approval by senior Justice Department officials.

On Tuesday, while testifying beside his father before a British select committee, James Murdoch denied having ever seen a key piece of evidence in the case that emerged in 2008 — an e-mail suggesting phone hacking went as high as the tabloid’s chief correspondent.

But after two former News Corp. executives cast doubt on his assertion — saying they personally had shown the younger Murdoch the e-mail in question – several British lawmakers insisted he should be recalled to address the discrepancy.

On Friday, Cameron, who himself is under pressure for his close ties to News Corp. executives arrested over the phone-hacking scandal, echoed those calls.

“Clearly, James Murdoch has got questions to answer in Parliament, and I’m sure that he will do that,” Cameron said. “News International has got some big issues to deal with and a mess to clear up.”

But Murdoch, in a statement, said, “I stand behind my testimony to the select committee.” News Corp. officials would not comment further, declining to say whether the younger Murdoch would agree to reappear before Parliament.

Contradictions to Murdoch’s testimony emerged Thursday, when Colin Myler, former editor of the News of the World, and Tom Crone, the former legal director at the tabloid, issued a statement effectively claiming the younger Murdoch had lied.

The two said they showed Murdoch the e-mail, which was included in sealed court documents in the settlement of a 2008 lawsuit brought by Gordon Taylor, the executive director of Britain’s professional soccer players union, whose phone was allegedly hacked by the News of the World. Taylor received more than $1.3 million in an out-of-court settlement, which some lawmakers now allege amounted to hush money to keep a lid on the scandal.

Titled “For Neville,” the e-mail mentioned a transcript of a hacked conversation allegedly prepared for Neville Thurlbeck, the paper’s chief correspondent. The e-mail — which Murdoch insists he never saw — is considered by lawmakers to be among the strongest pieces of hard evidence indicating that illegal hacking was not an isolated case.

Murdoch and other News Corp. officials have maintained that until relatively recently, they believed News of the World’s hacking had been limited to one 2005 incident, in which Prince William’s phone messages were intercepted by the tabloid’s royal correspondent and a private investigator.

The suggestion that Murdoch may have known about the “For Neville” e-mail infuriated lawmakers. Tom Watson, a member of the opposition Labor Party who specifically asked Murdoch on Tuesday about the e-mail, said on Friday that he had now referred the question to investigators at Scotland Yard.

The Justice Department and the FBI declined to comment on the possible issuance of sub­poenas.

Julie Henderson, a News Corp. spokeswoman, also declined to comment on the matter. But she said the company has “not seen any evidence to suggest there was any hacking of 9/11 victims’ phones.”

Markon reported from Washington.