The scandal has even embarrassed Prime Minister David Cameron, who hired Coulson as his director of communications and was a personal friend of Brooks.
Asked for his reaction to Murdoch's latest resignation, Cameron said: "Well, it's obviously a matter for him, and a matter for the company, and of course its shareholders."
James Murdoch was chairman of News International when the company settled two big phone hacking claims. Murdoch said he was unaware that hacking was widespread at the News of the World, which at the time blamed the problem on a single rogue reporter.
His father shut down the tabloid in July. Another Murdoch tabloid, The Sun, has also been at the center of the hacking scandal.
News International has settled about 60 lawsuits by phone-hacking targets, at a cost of millions of dollars (pounds). Some 60 more claims are being prepared.
When James Murdoch was re-elected chairman of BSkyB in November, 81 percent of shareholders supported him, a strong mark of disquiet given the near-unanimous votes accorded to other corporate chairs. A month earlier, he was re-elected to the News Corp. board, though 35 percent of the votes went against him, another noticeable stirring of discontent.
Despite Tuesday's resignation, the younger Murdoch appeared to still have the support of his father, who controls News Corp. through a family trust that will one day come under the command of his four oldest children, including James.
In a statement, Rupert Murdoch and Chief Operating Officer Chase Carey said they were "grateful" for James Murdoch's leadership of BSkyB and looked forward to his "continued substantial contributions at News Corp."
Some said Tuesday's resignation was not a surprise.
"I had expected actually that he would have stepped down at the time it was announced he was returning to New York and it is perhaps surprising that it has taken this long," said John Whittingdale, the Culture, Media and Sport chairman.
Business Writer Ryan Nakashima in Los Angeles contributed to this report.
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