A string of shareholders, including a British lawmaker who spearheaded the probe into the scandal, lined up to call for Murdoch and his sons to lose some or all of their power on the media giant's board of directors.
But Murdoch owns nearly 40 percent of voting shares and is backed by a Saudi royal with another seven percent, so the 15-member board including Murdoch and sons James and Lachlan was re-elected at the annual stockholders' meeting.
A proposal to strip the 80-year-old of his role as chairman was defeated, while plans by the board of directors to retain control over executive pay were approved, according to voting results released a few hours after the meeting.
Murdoch repeatedly voiced contrition and vowed to get to the bottom of the British scandal, but appeared irritated at one or two more vociferous critics.
"You've been treating us like mushrooms for a long time," said Stephen Mayne, head of the Australian Shareholders Association, at the 90-minute meeting held at News Corp.'s Fox Studios in Los Angeles.
"You're still trying to do it," he added, in repeated exchanges with the 80-year-old News Corporation head who chaired the meeting of a few hundred shareholders in a movie theater on the Fox lot.
Tom Watson, the head of the British parliamentary committee where Murdoch was hit by a foam pie protestor in July, said more alleged hacking details were expected to come out, which News Corp. investors should know about.
"I believe that people working for News International commissioned private investigators to obtain information through computer hacking," he said, adding that the victims included a former army intelligence officer.
"I think that that could expose this company to huge costs when it comes to civil litigation ... the board (of directors) have a duty to let shareholders know that," he added.
Murdoch started the meeting by another mea culpa about the hacking scandal,
while also saying it should be seen in the context of News Corp.'s overall commercial success.
"We cannot just be a profitable company, we must be a principled company ... We must admit to and confront our mistakes and establish a rigorous and
vigorous procedure to put things right," he said.
"There is simply no excuse for such unethical behavior," he said of the hacking of cellphones by journalists from the now-shuttered British tabloid weekly The News of the World.
Shortly before Murdoch's appearance, News Corp.'s British newspaper arm News International confirmed it would pay £2 million ($3.2 million, 2.3 million euros) to the family of a murdered girl at the heart of the hacking scandal.
In a joint statement with the family of Milly Dowler, Murdoch said he would personally donate £1 million to charities chosen by the family.
Reports of the settlement by News International first emerged in September but had not been confirmed by the firm.
The 168-year-old News of the World was shut down after a public outcry when it emerged a private investigator working for the paper hacked into Dowler's voicemail after she went missing in 2002.
At Friday's meeting in LA, Murdoch said: "These are real issues that we must confront and are confronting... If we hold others to account we must hold ourselves to account."
"I am personally determined to right whatever wrong has been committed and to make sure that it doesn't happen again anywhere in our company," he said.
As the meeting got underway inside the sprawling Fox studios -- where the Simpsons is made, among other shows -- outside scores of demonstrators protested the News Corp. gathering.
"Rupert isn't above the law," read one placard while another beamed in a Murdoch mask -- although many seemed to have come from the New York-inspired "Occupy LA" protests, held in downtown LA for the last week or two.