"Thousands" of celebrities and politicians were allegedly targeted
The News of the World has rejected claims its reporters regularly hack into the phones of celebrities and politicians to get stories.
It follows allegations in the Guardian that private investigators were hired to illegally intercept voicemails on "thousands" of people's mobile phones.
The tabloid has admitted paying damages in one case over phone hacking but it denied the practice was widespread.
The Guardian names a second person allegedly involved in a similar case.
The Guardian claims costs and damages were secretly paid to Jo Armstrong, the legal adviser to the Professional Footballers Association (PFA), on condition that she signed a confidentiality agreement.
It alleges the tabloid paid a total of £1m to settle legal cases which threatened to expose the use of illegal methods to break stories.
News International, which publishes the News of the World, has confirmed it paid damages to PFA chief executive Gordon Taylor.
It said that apart from the incidents which led to the jailing of the paper's royal editor and a private investigator in 2007, and the subsequent legal action involving Mr Taylor, there was no evidence to support the Guardian's allegations.
In a statement, it expressed confidence that there were no fresh cases of voicemails being accessed by News of the World journalists or private investigators instructed by its staff.
"It goes without saying that had the police uncovered such evidence, charges would have been brought against other News of the World personnel," the company said.
"Not only have there been no such charges, but the police have not considered it necessary to arrest or question any other member of News of the World staff."
News International accused the Guardian of being "selective and misleading".
The Guardian welcomed what it called the first confirmation from the group that it made an out-of-court settlement over the illegal interception of Mr Taylor's phone messages.
On Thursday, Met Assistant Commissioner John Yates said no new evidence had emerged since the original inquiry into phone hacking.
That 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.