Murdoch, pictured below, is expected to arrive in London towards the end of this week to deal with the latest crisis in his newspaper empire.
The future of the tabloid has been called into question after the deputy editor and four other journalists were detained yesterday on suspicion of making illegal payments to police officers and other officials, taking the total to 10.
The journalists are believed to be the paper's deputy editor, Geoff Webster, picture editor John Edwards, chief reporter John Kay, chief foreign correspondent Nick Parker and reporter John Sturgis.
They are being questioned at police stations in London and Wiltshire as part of the Operation Elveden investigation into payments to police.
It is unclear what evidence has prompted the police arrests or even when the alleged offences occurred.
The National Union of Journalists condemned the arrests and suggested there was now a "witch-hunt" against reporters.
Police said five men aged 45, 50, 68, 52 and 47 were arrested at their homes in London, Kent and Essex on suspicion of corruption, aiding and abetting misconduct in a public office, and conspiracy in relation to both offences.
The men were among eight people arrested. The others were described as being a serving member of the Armed Forces, a Ministry of Defence employee and a serving officer at Surrey Police, all in their 30s.
The arrests come just a fortnight after The Sun's former managing editor and three of its most senior journalists were held and later bailed over corruption allegations.
News International is still reeling from the closure of The Sun's sister title, the News of the World, last year, after it emerged that journalists had hacked the phone of murdered schoolgirl Milly Dowler.
In an internal memo to staff at News International, which also owns The Times and Sunday Times, chief executive Tom Mockridge said he had had a "personal assurance" from Rupert Murdoch yesterday that he plans to continue to own and publish The Sun.
Mockridge added: "Some of the individuals arrested have been instrumental in breaking important stories about public bodies, for example the scandal of our under- resourced troops in Iraq.
"We must take care not to pre-judge the outcome of the police interviews. It is vitally important for all those involved that proper due process should take its course. The company has provided legal support to those interviewed today."
It is expected Murdoch will visit staff in London towards the end of the week.
At lunchtime, The Sun's editor, Dominic Mohan, issued a public statement making it clear he would stay on, saying he was "determined to lead The Sun through these difficult times" and that "our focus is on putting out Monday's newspaper".
A statement from News Corporation, parent company of News International, said its Management and Standards Committee (MSC) had provided information to the Elveden investigation which led to the arrests and had also provided the option of "immediate legal representation" to those arrested.
The group said: "News Corporation remains committed to ensuring that unacceptable news-gathering practices by individuals in the past will not be repeated and last summer authorised the MSC to co-operate with the relevant authorities.
"The MSC will continue to ensure that all appropriate steps are taken to protect legitimate journalistic privilege and sources, private or personal information and legal privilege.
"News Corporation maintains its total support to the ongoing work of the MSC and is committed to making certain that legitimate journalism is vigorously pursued in both the public interest and in full compliance with the law."
It is understood there is growing anger among employees about the passing of information to police by management. The mood among reporters was, in the words of one, "stunned", coupled with a worry as to where this will end.
The National Union of Journalists warned that the reputation of those arrested will "inevitably" be damaged.
NUJ general secretary Michelle Stanistreet said: "Journalists are reeling at seeing five more of their colleagues thrown to the wolves in what many sense to be a witch-hunt.
"They are furious at what they see as a monumental betrayal on the part of News International. Once again Rupert Murdoch is trying to pin the blame on individual journalists, hoping that a few scalps will salvage his corporate reputation."
The homes of those arrested were being searched and officers were also carrying out searches at the offices of News International in Wapping, east London.
The arrests come two weeks after four former and current Sun journalists and a serving Metropolitan Police officer were arrested over alleged illegal police payments. Senior Sun employees Chris Pharo, 42, and Mike Sullivan, along with former executives Fergus Shanahan, 57, and Graham Dudman, were named by sources as suspects facing corruption allegations. All five were released on bail.
Surrey Police confirmed a serving officer was arrested at their home yesterday as part of Operation Elveden.
A spokesman said: "Surrey Police has been working closely with Operation Elveden since it was established in 2011, with a number of its officers seconded to the MPS [Metropolitan Police Service] to assist with the investigations.
"On learning about the involvement of one of its officers, the force immediately referred the matter to the Independent Police Complaints Commission (IPCC)."
The MoD refused to comment.
Operation Elveden, which runs alongside the Met's Operation Weeting team, was launched as the phone-hacking scandal erupted last July with allegations about the now-defunct News of the World targeting Milly Dowler's mobile phone.
The latest arrests mark a widening of the operation to investigate evidence in relation to suspected corruption involving public officials who are not police officers.
Deborah Glass, deputy chairwoman of the IPCC, said: "We are continuing to actively supervise the Metropolitan Police Service investigation into alleged corruption, including the latest referral from Surrey Police.
"The arrests are further evidence of the strenuous efforts being undertaken to identify police officers who may have taken corrupt payments."