Rupert Murdoch was "humbled" and held his head in his hands as he apologised to Milly Dowler's family for the hacking of the murdered schoolgirl's phone by the News of the World.
The media mogul gave a "full and sincere apology" to Milly's parents, Sally and Bob, and her sister Gemma at a meeting in a central London hotel, family lawyer Mark Lewis said.
Police claims that the teenager's voicemails were illegally intercepted by a private investigator working for the News of the World after she went missing in 2002 triggered a string of damaging revelations which led to the closure of the Sunday tabloid.
Flanked by the Dowlers, Mr Lewis described Mr Murdoch's repeated apologies during the meeting at the five-star One Aldwych hotel.
He said: "He was humbled to give a full and sincere apology to the Dowler family. The Dowler family told him that his papers should lead the way to set the standards of honesty and decency in the field, and not what had gone on before. At the end of the day, actions are going to speak louder than words."
He added: "He apologised many times. I don't think anybody could have held their head in their hands so many times."
Mr Murdoch said the News of the World's actions were "not the standard set by his father, a respected journalist, not the standard set by his mother", the Dowlers' lawyer said.
The Dowlers - who found out about Milly being targeted shortly before her killer, Levi Bellfield, went on trial at the Old Bailey - were the first of a string of crime victims to have been exposed as targets of the paper.
It is alleged that Milly's voicemail was accessed on behalf of the News of the World while she was missing, and that messages were deleted to make room for more recordings. This gave the family false hope that she was still alive.
Mr Murdoch emerged from the hotel to shouts of "shame on you" from a handful of protesters. The 80-year-old said: "As founder of the company I was appalled to find out what had happened and I apologised."