• News International chief executive tells staff she will not quit • Press complaints boss says News of the World lied to inquiry • Miliband calls on Brooks to consider 'her position'

Rebekah Brooks has told employees it is "inconceivable" she knew that the News of the World hacked into Milly Dowler's mobile phone.

The News International chief executive said she was "sickened" by the events, but insisted she was "determined to lead the company" – despite calls for her to resign.

Ed Miliband said Brooks should "consider her position" and has called for a public inquiry after the Guardian revealed the News of the World illegally accessed Dowler's voicemail messages under Brooks's editorship [see footnote]. David Cameron earlier described the hacking as a "truly dreadful act" and urged police to "pursue this in the most vigorous way", while the home secretary, Theresa May, said anyone who could commit such hacking was "sick".

Brooks, who was editing the paper at the time, emailed employees today to tell them: "It is inconceivable that I knew or worse, sanctioned these appalling allegations. I am aware of the speculation about my position. Therefore it is important you all know that as chief executive, I am determined to lead the company to ensure we do the right thing and resolve these serious issues."

Brooks said she has written to Milly Dowler's parents on Tuesday morning "to assure them News International will vigorously pursue the truth and that they will be the first to be informed of the outcome of our investigation".

She added: "I am sickened that these events are alleged to have happened. Not just because I was editor of the News of the World at the time, but if the accusations are true, the devastating effect on Milly Dowler's family is unforgivable."

Senior executives at News International discussed the Dowler revelations at a meeting with police this morning to talk about Scotland Yard's ongoing investigation into phone hacking. News International said Rebekah Brooks was not present at the meeting.

A senior source at the News of the World's owner said it was a pre-arranged meeting with officers from Operation Weeting, the Met's investigation into phone hacking that began at the start of the year.

Brooks said in her email: "This morning, in our regular Operation Weeting meeting, we have offered the MPS our full co-operation to establish the veracity of these fresh allegations."

Miliband had earlier called for a public inquiry and said Brooks should "consider her conscience and consider her position", as pressure mounts on the chief executive.

Meanwhile, the Press Complaints Commission chairwoman Peta Buscombe said she was lied to by the News of the World over phone hacking.

Buscombe had said in 2009 that the PCC was not misled by the News of the World during its own inquiry into phone hacking. However, on the BBC's Daily Politics show, she admitted she had been "misled by the News of the World".

"There's only so much we can do when people are lying to us. We know now that I was not being given the truth by the News of the World," Buscombe said. She denied having sided with the newspaper.

Miliband said the latest revelations in the News of the World phone-hacking saga were a "stain" on news reporting in the country. He added that the hacking "represents one of the darkest days in British journalism".

Earlier Cameron, currently in Afghanistan, said of the Guardian's revelation that the News of the World illegally targeted Milly Dowler and her family: "If they are true this is a truly dreadful act and a truly dreadful situation."

He added: "There is a police investigation into hacking allegations … they should investigate this without any fear, without any favour, without any worry about where the evidence should lead them.

"They should pursue this in the most vigorous way that they can in order to get to the truth of what happened. That is the absolute priority as a police investigation."

The home secretary told the home affairs select committee the revelations were "totally shocking" but said she did not know if the News of the World used hacking in relation to the Soham murders.

May was asked if there should be a public inquiry into the affair, but said the ongoing police investigation should be allowed to run.

The Metropolitan police commissioner, Sir Paul Stephenson, whose force is accused of not investigating phone hacking properly in the first place, said on Tuesday: "My heart goes out to the Dowler family."

He told BBC London: "I have to be very careful to say nothing that could prejudice our live investigation but if it is proved to be true, then irrespective of the legality or illegality of it, I'm not sure there is anyone who wouldn't be appalled and repulsed by such behaviour."

Former deputy prime minister Lord Prescott said on Twitter that he would write to the culture secretary, Jeremy Hunt, demanding he block News Corp's bid to take full control of pay-TV company BSkyB following the revelations about Dowler.

However, John Whittingdale, the chairman of the culture, media and sport select committee, told BBC Radio 4's Today programme that phone hacking at the News of the World should not taint the rest of Rupert Murdoch's empire. "You cannot necessarily condemn the entire of News Corp just because of the actions of some individuals in another part of the organisation," he said.

"News International is a part of News Corp but it's a different part. News Corp is a global enterprise and I don't think one should condemn the entire organisation because something very clearly was going wrong in the News of the World."

Detectives from Operation Weeting are believed to have found evidence of the targeting of the Dowlers in a collection of 11,000 pages of notes kept by Glenn Mulcaire, the private investigator jailed for phone hacking on behalf of the News of the World.

In the past four weeks Met officers have approached Surrey police and taken formal statements from some of those involved in the original inquiry, who were concerned about how News of the World journalists intercepted – and deleted – the voicemail messages of Milly Dowler.

The messages were deleted by journalists in the first few days after Milly's disappearance to create space for more messages. As a result friends and relatives of Milly concluded wrongly she might still be alive [see footnote]. Police also feared evidence may have been destroyed.

• The following was published on 12 December 2011 in the corrections and clarifications column: An article about the investigation into the abduction and death of Milly Dowler (News of the World hacked Milly Dowler's phone during police hunt, 5 July, page 1) stated that voicemail "messages were deleted by [NoW] journalists in the first few days after Milly's disappearance in order to free up space for more messages. As a result friends and relatives of Milly concluded wrongly that she might still be alive." Since this story was published new evidence – as reported in the Guardian of 10 December – has led the Metropolitan police to believe that this was unlikely to have been correct and that while the News of the World hacked Milly Dowler's phone the newspaper is unlikely to have been responsible for the deletion of a set of voicemails from the phone that caused her parents to have false hopes that she was alive, according to a Metropolitan police statement made to the Leveson inquiry on 12 December.