Ed Miliband has said ex-News of the World editor Rebekah Brooks must "consider her position" over claims Milly Dowler's phone was hacked.
The Labour leader said Mrs Brooks, now chief executive of the paper's parent company News International, should "examine her conscience".
Mrs Brooks said it was "inconceivable" she knew about the alleged hacking of the murdered teenager's mobile.
MPs will debate calls for a public inquiry into the issue on Wednesday.
Downing Street has declined to comment on Mrs Brooks' position "while a police investigation is ongoing", but the prime minister has described the allegations as "truly dreadful".
The Guardian claims that Milly's voicemail was hacked into by an investigator working for the News of the World, after she disappeared in 2002 and that messages which had already been listened to were deleted, to make room for more to be left.
Mrs Brooks, who is chief executive of Rupert Murdoch's UK operation, News International, was editor of the News of the World at the time.
In a statement to News International staff, Mrs Brooks said: "It is almost too horrific to believe that a professional journalist or even a freelance inquiry agent working on behalf of a member of the News of the World staff could behave in this way.
"If the allegations are proved to be true then I can promise the strongest possible action will be taken as this company will not tolerate such disgraceful behaviour.
"I hope that you all realise it is inconceivable that I knew or worse, sanctioned these appalling allegations."
It has also emerged that detectives investigating the phone hacking claims have contacted the parents of murdered schoolgirls Holly Wells and Jessica Chapman.
Mr Miliband called for a public inquiry to be held once police investigations had been completed.
He said: "Of course she [Mrs Brooks] should consider her position but this goes well beyond one individual.
"This is about the culture and practices, which were obviously going on at that newspaper, the News of the World, over a sustained period of time."
News International executives should "start taking responsibility for this", he said.
Mr Miliband said of Mrs Brooks: "She should examine her conscience, and I think she will, as this happened on her watch. It's not about one incident but what was happening systematically at a newspaper."
In the Commons Deputy Labour leader Harriet Harman urged the government to back a "full public inquiry into illegality in the newspaper industry".
And the issue was raised in the House of Lords when former Conservative Party chairman Lord Fowler called on the government to set up an independent inquiry into the ethics of the media, after what he called "one of the biggest scandals affecting the press in living memory".
Prime Minister David Cameron said the alleged hacking was a "truly dreadful act" and urged the police to pursue their criminal investigation into alleged phone hacking by journalists in "the most vigorous way they can". Deputy PM Nick Clegg said if true, the behaviour of those involved was "simply beneath contempt".
Until the allegations about Milly's voicemail, the News of the World hacking scandal had focused on claims involving the mobile phones of celebrities.
Milly went missing in March 2002 and her body was discovered six months later. Nightclub bouncer Levi Bellfield was convicted of her murder last month.
Lawyers acting for the Dowler family say that the deletion of messages from Milly's phone after her disappearance could have led relatives to hold "false hope" that the teenager was still alive, increasing their eventual agony.
Labour MP Chris Bryant suggested it was an example of a "national newspaper playing God with a family's emotions" and was granted an urgent debate on calls for a public inquiry in the Commons on Wednesday.
Labour MP Tom Watson said there had been a "failure of political leadership" over phone-hacking, with senior politicians not acting quickly enough to investigate the problem.
He told the BBC: "They have let the Dowler family down by not calling for an inquiry. It's time they acted. And that's the biggest scandal of the lot. Politicians are frightened of News International and they need to act."
The chairman of the Press Complaints Commission, Baroness Buscombe, defended the body's actions over the phone-hacking allegations.
She told BBC Two's Daily Politics she was angry that the PCC had been misled by the News of the World and added: "There's only so much we can do when people are lying to us."