The deputy Labour leader made the comments after Paul McCartney's ex-wife Heather Mills told BBC's Newsnight that a Mirror Group editorial executive admitted in 2001 that her voicemail had been hacked.
Harman told Sky News: "[Piers Morgan] said he heard a 'heart-breaking' phone message, which clearly gives rise to the assumption that he'd heard a tape-recorded message.
"It is not good enough for him to say - or for someone to say on his behalf - 'I always complied with the law and the Press Complaints Commission code of conduct'. He's got to answer now we've got these allegations from Heather Mills."
Morgan had previously written an article in the Daily Mail which revealed that he had heard a phone message left by McCartney on Mills's phone while they were dating.
The former Mirror editor issued a statement which read: "The BBC has confirmed to me that this executive [named by Mills] was not employed by the Daily Mirror. I have no knowledge of any conversation any executive from other newspapers at Trinity Mirror may or may not have had with Heather Mills.
"What I can say and have knowledge of is that Sir Paul McCartney asserted that Heather Mills illegally intercepted his telephones, and leaked confidential material to the media. This is well documented, and was stated in their divorce case."
Morgan continued: "To reiterate, I have never hacked a phone, told anyone to hack a phone, nor to my knowledge published any story obtained from the hacking of a phone."
A Trinity Mirror spokesman added: "Our position is clear. All our journalists work within the criminal law and the PCC [Press Complaints Commission] code of conduct."
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