News Corporation chairman Rupert Murdoch is expected to fly to London next week after reassuring staff he would not sell The Sun in the wake of a second wave of arrests at the newspaper.
Five senior journalists were among eight people arrested over allegations of improper payments to police and public officials.
A serving police officer, a Ministry of Defence employee and a serving officer in the British army were also detained by police.
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 murdered schoolgirl Milly Dowler's mobile phone.
Today's arrests of Sun deputy editor Geoff Webster, picture editor John Edwards, chief reporter John Kay, chief foreign correspondent Nick Parker, and news editor John Sturgis sparked speculation that the red top would go the same way as the News of the World.
They follow the arrests two weeks ago of four current and former Sun employees, as well as a police officer.
However, a leaked memo from Tom Mockridge, chief executive of News International - part of News Corp - to staff said that Mr Murdoch had personally assured him of his "total commitment to continue to own and publish" the paper.
A News International spokeswoman said: "The statement sets out News Corporation and Rupert's position and support for News International and The Sun."
Mr Mockridge also said he had written to the Independent Police Complaints Commission (IPCC) to seek clarification about independent oversight of the police investigation.
The Sun editor Dominic Mohan said he was shocked by the developments but would focus on putting out Monday's edition.
The five journalists were released on bail to dates in May, while the other three men were released on bail to dates in March and May.
