Prime Minister David Cameron backed calls for a public inquiry into phone-hacking by the News of the World on Wednesday, amid claims that it targeted relatives of murdered children and victims of the London bombings.

But he said police should first complete their investigations into "absolutely disgusting" claims about the top-selling Sunday newspaper, owned by Rupert Murdoch's News International.

"We do need to have an inquiry, possibly inquiries into what has happened," Cameron told the House of Commons, adding that the probes should cover why an original police investigation into hacking in 2006 had failed to unearth the latest claims.

"Let us be clear -- we are no longer talking here about politicians and celebrities, we are talking about murder victims, potentially terrorist victims having their phones hacked into.

"It is absolutely disgusting what has taken place."

But he rejected calls by opposition Labour leader Ed Miliband for an immediate public inquiry "because you must not jeopardise the police investigation".

Cameron also refused to back Miliband's call for the resignation of Rebekah Brooks, the chief executive of News International who was editor of the News of the World in 2002, when the hacking is alleged to have occurred.

And he insisted the row should not affect the government's decision, due within days, on whether Murdoch's News Corp. should be able to proceed with its controversial bid to take full control of satellite broadcaster BSkyB.

News of the World has been dogged by claims of phone hacking since its royal editor and a private investigator were jailed for the practice in 2007, and fresh allegations sparked a new police investigation in January.

Most of the victims identified so far have been politicians and celebrities, but it has now emerged that relatives of those killed in the July 7, 2005 attacks on the London transport network were also targeted.

One of them, Graham Foulkes, whose son David died in the attacks, told the BBC that "the thought that somebody may have been listening to that (his voicemails) just looking for a cheap headline is just horrendous".

It has also emerged that the mobile phones of Holly Wells and Jessica Chapman, the two 10-year-olds who went missing in Soham, in 2002 and were found murdered several weeks later, may have been hacked.

The claims follow reports on Tuesday that murdered teenager Milly Dowler's voicemail was hacked after she went missing in 2002. Some of her messages were allegedly deleted, possibly hampering the police investigation.

Miliband called on Brooks to quit because she was editor of the News of the World at the time, saying: "She should take responsibility and stand down."

But Cameron replied: "What I think is we should let the police do their work, they must follow the evidence wherever it leads."

In an email to staff on Tuesday, Brooks promised a full investigation, saying she was "sickened" by the new allegations. But she defied calls to quit and said it was "inconceivable" she had sanctioned the hacking.

The row has already had financial repercussions: motor companies Ford and Vauxhall have suspended their advertising with the News of the World.

Miliband is also pushing for the government to reconsider plans to approve News Corp.'s bid for control of BSkyB "at a time when News International is subject to a major criminal investigation".

But Cameron insisted he would not interfere, saying: "What we have done here is follow absolutely to the letter the correct legal processes."

The prime minister himself, meanwhile, could be swept into the scandal through Andy Coulson, a former News of the World editor who worked as his director of communications until he resigned in January.

Police confirmed Wednesday they had received documents suggesting journalists at the tabloid had illegally paid police officers for information, reportedly during Coulson's time in charge.

Coulson has always denied wrongdoing but Miliband said Cameron had made a "catastrophic error of judgement" in hiring him.