The Times' own journalists have criticized its coverage of the BBC scandal, but it has published multiple stories about it.
Times columnist Joe Nocera asked in an Oct. 29 piece whether Thompson is "the right man for the job" and noted the ongoing investigation of Savile may distract him as the newspaper company's CEO.
"Since early October, all anybody has asked about Thompson are those two most damning of questions: what did he know, and when did he know it?" Nocera wrote.
The newspaper's public editor, Margaret Sullivan, had called on the company to pursue the story relentlessly, before she concluded in a blog post on Monday that "The Times has pulled no punches in reporting."
But as the BBC scandal has widened, media watchers such as news industry analyst Ken Doctor said Thompson should step aside "for the good of the Times."
Doctor, an analyst with Outsell, a global research and advisory firm, said there are "lingering questions about the extent that Thompson knew about the allegations."
"It's a major distraction for The New York Times, when The New York Times is in a huge transition mode for itself," Doctor said.
Nakashima reported from Los Angeles. AP Business Writer Tom Murphy in Indianapolis and AP Writer Cassandra Vinograd in London contributed to this story.
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