Publisher News International axed the 168-year-old tabloid in the wake of phone-hacking allegations last week.
The hacking group also said it hit other websites run by News International, News Corp.
She was made chief executive of News International in 2009 and resigned in July 2011.
BBC: Rebekah Brooks anger over charges in phone-hacking probe
Murdoch also confirmed that News International will launch a Sunday edition of The Sun.
Mr Darcey also told staff that News International would support Mr Webster through the legal process.
BBC: The Sun's Geoff Webster charged over payments to officials
Public outrage over the scandal led News International to close the best-selling Sunday tabloid.
Mr Wallis's arrest forced the Met to answer more questions about its relationship with News International.
And James smoothly used the ongoing investigations into News International to avoid answering questions.
News International said Thursday that some of the paper's 200 staff members may be laid off.
Brooks later became chief executive of News International, a UK subsidiary of Murdoch's News Corp. empire.
News International's papers combine a lot of readers with a willingness to swing both ways.
James Murdoch resigned as chairman of News International, the UK newspaper publishing arm of News Corp.
However, the largest effect is likely to be on the proposed takeover of BSkyB by News International.
News International confirmed that two of the latest arrests related to people currently working for the Sun.
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Parker was arrested earlier as part of the corruption investigation, the source close to News International said.
"The practices at News International have stained the proud tradition of the British press, " Ms. Harman said.
WSJ: James Murdoch Steps Down as Executive Chairman of News International
Former News International boss Rebekah Brooks has been formally charged over phone hacking, Scotland Yard has said.
It interviewed News International bosses after the Guardian claimed the practice was widespread at the Sunday tabloid.
Public outrage over the claims led News International to shut down the best-selling Sunday tabloid in July.
He was supported in his decision by Rupert Murdoch, boss of News Corporation which owns News International.
Now there are two reasons why News Corporation and News International were so keen to protect Rebekah Brooks.
For this to happen so soon after Brooks stepped down as CEO of News International, News Corp.
News International said it would co-operate fully with any potential criminal inquiries or civil proceedings which may arise.
News International is a subsidiary of News Corp and published the now-defunct News of the World (NoW) tabloid.
His resignation comes just hours after Rebekah Brooks stepped down as CEO of News International, News Corp.
So far, 10 people have been arrested, including, on Sunday, Rebekah Brooks, the head of News International.
Rebekah Brooks, the former News International chief who Murdoch backed until last week, was arrested yesterday in London.
News International, which is owned by Rupert Murdoch, has offered to co-operate fully with a Metropolitan Police inquiry.
That is probably the dumbest comment yet on the crisis at News International.
Les Hinton, the former chief executive of News International, which oversees News Corp.
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