Rupert Murdoch has issued an apology to the family of Milly Dowler, the missing teen whose voicemail was hacked by News of the World.

Dowler's family lawyer has said that Murdoch gave a full and sincere apology to the family for the actions of journalists at his newspaper, according to USA Today.

According to the report, Murdoch called a private meeting and apologized many times, telling the Dowler family that the events that transpired at the defunct News of the World tabloid weren't in line with the standards that were set when his father began in the media industry.

Mark Lewis has reportedly told reporters that Murdoch was very humbled, he was very shaken and he was very sincere.

Lewis added that the Dowlers told Murdoch that his newspapers should take the lead in setting the standard of honesty and decency in journalism, according to USA Today report.

News of Murdoch's apology came after his executive Rebekah Brooks resigned on Friday. Both Murdoch and Brooks have been facing political pressure since phone hacking and bribery allegations surfaced.

Brooks, 43, was editor of News of the World in 2002 when it is alleged that the paper hacked into the voicemail of 13-year-old Milly Dowler that year. Dowler was missing at the time and police was investigating the incident. It is believed that the hack impeded police investigation at the time. Dowler was eventually found dead.

Brooks said she didn't know if the phone hacking.

Brooks is a close friend of Murdoch, who described her as his first priority when he flew in to London this week to manage the crisis at News Corp's British newspaper unit. A News Corp veteran, New Zealander Tom Mockridge, who has spent the past eight years running the group's Sky Italia television interests in Italy, has acquired her position.

British Prime Minister David Cameron also came under pressure for his personal relationship with Brooks and for hiring another ex-editor of the News of the World as his spokesman, who was later arrested by police probing the investigation.

Murdoch, 80, has many ties to many British politicians that date back for years.

Members of Parliament in Britain have asked that Murdoch appear for a public inquiry on the phone hacking allegations, but Murdoch declined and said he would go before a separate inquiry initiated by Cameron and led by a judge.

Murdoch has also indicated his willingness to discuss other ways of giving evidence to parliament.