Labour deputy leader Harriet Harman said Thursday that Morgan "has got to answer" questions about phone hacking from when he was editor of the Daily Mirror from 1995 to 2004.
Harman said on Sky News: "It is not good enough for him to say - or somebody 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."
Tory MP Therese Coffey, who is on the parliamentary committee that is investigating the widespread phone hacking allegations, said Mills' allegations seemed "very strong" and she "didn't see any point in [Morgan] necessarily just staying in the U.S. and issuing statements."
"I just hope that the police take the evidence and go with it," she said, "and if Mr. Morgan wants to come back to the UK and help them with their inquiries, and I don't mean being arrested in any way, I'm sure he can add more light."
But John Whittingdale, who chairs the committee, said there are no plans to call Morgan before the committee -- and that the committee is focused on determining whether previous witnesses -- like News Corp's James Murdoch -- had provided misleading testimony.
Mills told the BBC Wednesday that a reporter working for a Trinity Mirror publication called her in 2001 with quotes from an apology voice message left for her by Paul McCartney while she was in India. When pressed, the reporter admitted the details of the message had been obtained through phone hacking.
According to the BBC the reporter in question was not Piers Morgan, but in 2006 Morgan wrote an article for the Mirror suggesting he had heard the voice message in question. "It was heartbreaking," Morgan wrote at the time. "The couple had clearly had a tiff, Heather had fled to India, and Paul was pleading with her to come back. He sounded lonely, miserable and desperate, and even sang 'We Can Work It Out' into the answer phone."
Morgan denied the allegations Wednesday in a statement through CNN:
Heather Mills has made unsubstantiated claims about a conversation she may or may not have had with a senior executive from a Trinity Mirror newspaper in 2001. The BBC has confirmed to me that this executive 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.
Trinity Mirror, which also publishes the Sunday Mirror and People, has launched an internal investigation into the allegations, but said in a statement: "Our position is clear. All our journalists work within the criminal law and the PCC [Press Complaints Commission] code of conduct."