Conservative leader David Cameron has insisted Andy Coulson's job as his communications director is safe.
Senior Labour and Lib Dems figures have said he should be fired after revelations about phone messages being intercepted by the News of the World.
The Guardian alleges up to 3,000 high profile figures - including ex-deputy PM John Prescott - were targeted by the paper Mr Coulson edited until 2007.
Asked if Mr Coulson's job was safe, Mr Cameron said: "Yes, of course."
Mr Cameron sought to make a distinction between what Mr Coulson may have done in the past and what he does now for the Conservative Party.
Speaking outside his home in West London, Mr Cameron said: "It's wrong for newspapers to breach people's privacy with no justification.
"That is why Andy Coulson resigned as editor of the News of the World two-and-a-half years ago. Of course I knew about that resignation before offering him the job. But I believe in giving people a second chance.
"As director of communications he does an excellent job for the Conservatives, in a proper, upright way at all times."
Following the Guardian's revelations, the police have come under pressure to launch a fresh investigation into the phone hacking claims.
But the Metropolitan Police said no new evidence had come to light to warrant this, adding that in the "vast majority" of cases there was no evidence to suggest the phones of alleged victims - including John Prescott - had been tapped.
In a statement, News International said it worked to ensure its staff operated within the law, but insisted its staff would not "shirk from vigorously defending our right and proper role to expose wrongdoing".
Mr Coulson, who has yet to comment on whether he knew about phone hacking at the paper, issued a statement on Wednesday saying "this story relates to an alleged payment made after I left the News of the World two and a half years ago. I have no knowledge whatsoever of any settlement with Gordon Taylor".
The Guardian revealed that the News of the World had reached an out-of-court settlement with Gordon Taylor, head of the Professional Footballers' Association, after hacking into his phone.
The Conservatives argue that calls by senior Labour figures such as Charles Clarke and John Prescott for Mr Coulson to be sacked were politically-motivated attempts to destabilise Mr Cameron.
Speaking on BBC's Question Time, shadow culture secretary Jeremy Hunt said the other parties had shown a "huge dose of political opportunism" over the issue.
"The reality is that Andy Coulson stepped down from editing the News of the World and he did it because he was taking responsibility for something he did not know about but something he wanted to take responsibility for," he said.
"He has behaved totally honourably."
Mr Prescott has written to Mr Cameron expressing his "deep concern" about the Guardian's allegation.
The former deputy prime minister, who has said he will contact the police over claims phone messages were intercepted by investigators hired by a News of the World reporter, said: "This really does call Cameron's judgement into question in hiring Coulson. The question Cameron must answer is 'do you back him or sack him?'"
But pressure is likely to continue on Mr Coulson after the Commons Culture Committee said it would re-open its inquiry into the affair.
Tory MP John Whittingdale, the committee's chairman, told the BBC there was "a strong likelihood that Mr Coulson will be one of those" the committee wanted to grill depending on what the evidence seen by The Guardian contained.
The Lib Dems have called for Mr Coulson to be sacked, comparing his case to that of Damian McBride, the Downing Street aide forced to quit over e-mail smears against senior Conservatives.
"It's extraordinary that the leader of the opposition, who wants to be a prime minister, employs Andy Coulson who, at best, was responsible for a newspaper that was out of control and, at worst, was personally implicated in criminal activity," its home affairs spokesman Chris Huhne said.
"The exact parallel is surely with Damian McBride. If the prime minister was right to sack Damian McBride, should the leader of the opposition not sack Andy Coulson?"
Labour MP Denis MacShane called for a Commons investigation, with evidence given on oath, and questioned why Mr Coulson still had a House of Commons pass.
Labour's Ann Clwyd called on Mr Coulson to be stripped of his Commons pass while the latest allegations are investigated.
"Given Mr Coulson's dubious reputation, none of us on this side of the House can feel comfortable while he is allowed to wander the corridors here. Can we not, at the very least, while he is under suspicion, take his pass away from him?," she told MPs.
Home Office minister David Hanson said such issues were a "matter for the House authorities".
Shadow Home Secretary Chris Grayling said - to laughter from the Labour and Lib Dem benches - that there was "no doubt that the story that appeared in this morning's newspaper raised questions".
But he called for a "measured response" to the allegations and said it should be left to the police to "decide whether there is any new information that warrants further action".
In the Lords, security minister Lord West said the police's decision not to launch a new investigation was "slightly surprising", adding: "I would jolly well like to know if some blighter was trying to do that to me."
Business Secretary Lord Mandelson told BBC London it would defy belief if Mr Coulson, as the editor of the News of the World, did not know what was going on in the newspaper and the methods that were being used.
BBC political editor Nick Robinson said the problem Mr Cameron faces was that new questions were now being opened about the past.
He said Mr Coulson had "already broken rule one for any spin doctor - 'Never become the story,' adding: "He's good enough at his job to know that this story could soon become one about David Cameron's judgement."