"Thousands" of celebrities and politicians were allegedly targeted
The News of the World's publisher has said it will "refute" allegations of widespread illegal phone tapping.
News International's new chief executive Rebekah Wade said it welcomed the chance to appear before MPs on the Commons culture committee on 21 July.
The Metropolitan Police said it had started contacting people whose phones may have been hacked to warn them of what might have happened.
The Guardian claimed the Sunday paper used phone hacking to obtain stories.
Ms Wade, who is currently editor of the Sun but will take on the News International post in September, said News of the World editor Colin Myler and legal counsel Tom Crone would represent the company to answer questions about the allegations before the committee.
She said the company believed the Guardian coverage had substantially - and likely deliberately - misled the public.
In a letter to the culture, media and sport committee's chairman John Whittingdale, she said: "It [the Guardian] is rushing out high volumes of coverage and repeating allegations by such sources as unnamed Met officers implying that 'thousands' of individuals were the object of illegal phone hacking, an assertion that is roundly contradicted by the Met Assistant Commissioner's statement yesterday."
'Judge and jury'
Met Assistant Commissioner John Yates said on Thursday that he wanted to ensure the force had taken all proper steps to ensure people had been informed about the possibility of their phones having been tapped.
He also said that no new evidence had emerged since an original inquiry into phone hacking resulted in News of the World royal editor Clive Goodman and private investigator Glen Mulcaire being jailed for four and six months respectively in January 2007.
Liberal Democrat home affairs spokesman Chris Huhne has submitted a formal request to the Independent Police Complaints Commission (IPCC) to mount an inquiry into the Met's decision not to reinvestigate allegations of phone hacking.
Mr Huhne said: "The Metropolitan Police cannot act as judge and jury in its own trial.
"Only an independent inquiry can properly consider any possible neglect of duty by the specialist operations department into the original investigation."
The IPCC said it had not yet made a decision on whether to proceed with an inquiry.
Director of Public Prosecutions Keir Starmer QC has said the Crown Prosecution Service will carry out an "urgent examination" of files to check they were properly dealt with at the time.
Chancellor Alistair Darling said the alleged actions of journalists working for the News of the World were "unforgivable".
He told the BBC: "It's for the Crown Prosecution Service, which has said that it's looking at these allegations now, to decide whether or not there needs to be further investigations.
"But I think most people would believe that there are questions here that need to be answered. This is a very serious allegation concerning people's privacy and I hope that the Crown Prosecution Service will get on with it as soon as it can."
The Guardian said the phone hacking was far more widespread, affecting "thousands" of celebrities and politicians.
These were said to include former deputy prime minister John Prescott, London Mayor Boris Johnson, former Culture Secretary Tessa Jowell, actress Gwyneth Paltrow, model Elle Macpherson and publicist Max Clifford.
The Guardian claimed the tabloid paid £1m to settle legal cases which threatened to expose the use of illegal methods to get stories.
In its latest revelations, the Guardian named Manchester United manager Sir Alex Ferguson and former England captain Alan Shearer among those whose messages were allegedly intercepted.
One lawyer told the BBC he had had two inquiries from public figures who considering suing the paper and that more were seeking advice.