The private investigator at the centre of the News of the World phone-hacking scandal has issued a public apology to all those who have been hurt or upset by his activity.

In a statement released exclusively to the Guardian, Glenn Mulcaire made no direct reference to the hacking of Milly Dowler's phone, but he said he had never intended to interfere with any police inquiry.

"I want to apologise to anybody who was hurt or upset by what I have done," he said, adding that he had worked at the NoW under "constant demand for results".

He released the statement at the Guardian's request after experiencing what he described as "vilification" following the revelation of the hacking of the missing schoolgirl's phone.

"Much has been published in the media about me. Up to now, I have not responded publicly in any way to all the stories but in the light of the publicity over the last 24 hours, I feel I must break my silence.

"I want to apologise to anybody who was hurt or upset by what I have done. I've been to court. I've pleaded guilty. And I've gone to prison and been punished. I still face the possibility of further criminal prosecution.

"Working for the News of the World was never easy. There was relentless pressure. There was a constant demand for results. I knew what we did pushed the limits ethically. But, at the time, I didn't understand that I had broken the law at all.

"A lot of information I obtained was simply tittle-tattle, of no great importance to anyone, but sometimes what I did was for what I thought was the greater good, to carry out investigative journalism.

"I never had any intention of interfering with any police inquiry into any crime.

"I know I have brought the vilification I am experiencing upon myself, but I do ask the media to leave my family and my children, who are all blameless, alone."

The statement came as it emerged the parents of Holly Wells and Jessica Chapman, the two children murdered by Ian Huntley, were contacted by Scotland Yard detectives investigating phone hacking at the NoW.

Earlier Rebekah Brooks, chief executive of News International, told employees it was "inconceivable" she knew that NoW, which she edited at the time, hacked into Milly Dowler's mobile phone.

On Wednesday there will be a rare emergency Commons debate into calls for a public inquiry into phone hacking by News International journalists, and a potential cover up by its senior executives.