Amid mounting pressure for an official government statement, Commons Speaker John Bercow approved an urgent question from Labour former minister Tom Watson.
It came after Downing Street communications chief Andy Coulson, the former editor of the News of the World, told police he would be happy to meet them voluntarily to discuss fresh allegations.
Fresh attention has been focused on the case after a former NoW journalist Sean Hoare claimed Mr Coulson knew of eavesdropping tactics used at the newspaper during his time in charge.
Downing Street said the Prime Minister retained full confidence in Mr Coulson, who has consistently denied the claims, and that the new allegations made no difference to his position.
A spokesman for Mr Coulson said he had not been contacted by the police but was "happy to voluntarily meet with them following allegations made by Sean Hoare.
"Mr Coulson emphatically denies these allegations. He has, however, offered to talk to officers if the need arises and would welcome the opportunity to give his view on Mr Hoare's claims."
Metropolitan Police Assistant Commissioner John Yates said today that he would be prepared to investigate Mr Hoare's allegations, which first surfaced in the New York Times.
Labour MPs and ex-deputy prime minister Lord Prescott have called for a fresh inquiry, and Lord Prescott is also seeking clarification from the Met over whether his phone was tapped.
The Speaker's office said Mr Bercow had granted Mr Watson's request for an urgent question about "the Metropolitan Police investigation into phone hacking by the News of the World".
Mr Watson has been among the most prominent MPs calling for the investigation to be reopened - accusing the police of "dragging their feet".
Mr Coulson came under renewed pressure last week after former journalists told the US paper that the use of phone hacking was far more extensive than the News of the World acknowledged.
The NoW's former royal editor, Clive Goodman, and a private investigator used by the newspaper were jailed in 2007 following phone hacking disclosures.
Mr Coulson said at the time that he had not known of the practice but resigned his editorship, before joining then Tory leader David Cameron as communications boss, moving with him into No 10.
Friends of Mr Coulson were keen to stress today that his statement was not prompted by a police approach, and pointed out that a new investigation had not yet even been launched by Scotland Yard.
Mr Yates told BBC Radio 4's Today programme that Mr Hoare's allegation would be considered by the police following consultation with the Crown Prosecution Service.
"This is the first time we have heard of Mr Hoare or anything he has to say. We focused our resources where we thought we could get the best evidence," he said - expressing surprise that the force had not been alerted earlier by the US newspaper.
He denied the original probe had been mishandled, insisting it had been "very, very thorough".
"It resulted in the conviction of two people, it resulted in a very complex area of law being clarified and it sent an extremely strong deterrent to other people," he said.
He refused to speculate on how many people's phones may have been hacked but stressed : "All I would say is we take our obligations regarding telling victims very seriously.
"There's a misunderstanding here that suggests just because your name features in a private investigator's files, your phone has been hacked.
"The fact that John Prescott's name appears on an invoice does not mean his phone has been hacked. It means he is of interest to a private investigator. That's what private investigators do.
"I believe there is no evidence that his phone has been hacked. I have made that very clear on a number of occasions."
Mr Watson said: "Never mind asking the New York Times for their transcripts, John Yates should be conducting his own interviews. Two former News of the World journalists have admitted witnessing phone hacking, and a parliamentary inquiry confirmed another senior journalist had transcribed illegally hacked phone messages. None of them have been interviewed by the police.
"Yates is dragging his feet. He should get on with investigating these important new leads."
The Prime Minister's spokesman said Mr Cameron was "completely happy with the job Mr Coulson is doing".
"The reports that have been in the media over the weekend do not change the situation for the Prime Minister. Andy Coulson has been clear in denying the allegations that have been made.
"Clearly, if the police want to look at this, then that is a matter for them and we would not want to interfere," the spokesman added.
Mr Yates is bound to be questioned about the phone-hacking affair when he appears before MPs at the Commons Home Affairs Select Committee tomorrow afternoon, in his role as the yard's Assistant Commissioner for Specialist Operations.
He is due to answer questions about "topical aspects of his role".
In a statement released today the News of the World accused the New York Times of being motivated by commercial rivalry.
It said: "The News of the World repeatedly asked the New York Times to provide evidence to support their allegations and they were unable to do so.
"Indeed, the story they published contained no new credible evidence and relied heavily on anonymous sources, contrary to the paper's own editorial guidelines.
"In so doing, they have undermined their own reputation and confirmed our suspicion their story was motivated by commercial rivalry.
"We reject absolutely any suggestion there was a widespread culture of wrongdoing at the News of the World."
Ex-home secretary Alan Johnson told BBC Radio 4's The World At One: "I think this is a matter that Parliament should discuss.
"What we have now is the New York Times report that says they have spoken to at least a dozen former reporters, one former editor, that said this was all-pervasive and went much wider than this one journalist and one private detective."
Chairman of the Commons Culture, Media and Sport Committee, Tory MP John Whittingdale, said his committee would not be reopening its probe into the affair.
He told the programme: "The Labour figures who have jumped on this bandwagon are doing so with a certain amount of political opportunism."
And he added: "It wouldn't be right for the Home Secretary of any party to intervene. This is a matter for the police."
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