The media mogul also confirmed he will begin publishing the top-selling tabloid seven days a week by launching a new paper called the Sun on Sunday "very soon".
The Sun has been rocked by the arrests of 10 current and former senior reporters and executives since November over alleged corrupt payments to public officials.
Mr Murdoch, who is visiting the headquarters of his British newspapers in Wapping, east London, sought to reassure Sun staff in a memo (click here to read it).
He wrote: "I have immense respect for our heritage, your exceptional journalism and, above all, you, the talented women and men who work tirelessly every day to ensure our readers have access to such a trusted news source.
"I believe this newsroom is full of great journalists and I remain grateful for your superb work and for the stories you uncover to inform and protect the public."
He said the recent arrests - including nine in the past three weeks, among them The Sun's deputy editor, picture editor and chief reporter - were "a source of great pain" for him.
Some Sun journalists have expressed anger that News Corporation's Management Standards Committee (MSC) - formed to clean up the company following the phone-hacking scandal - gave police the information that led to the arrests.
Mr Murdoch said illegal activities "simply cannot and will not be tolerated" but insisted that journalists' "legitimate" confidential sources would be protected.
He wrote: "I made a commitment last summer that I would do everything I could to get to the bottom of our problems and make this company an example to Fleet Street of ethical journalism.
"We will continue to ensure that all appropriate steps are taken to protect legitimate journalistic privilege and sources, which I know are essential for all of you to do your jobs.
"But we cannot protect people who have paid public officials."
The media tycoon added: "We will turn over every piece of evidence we find - not just because we are obligated to but because it is the right thing to do.
"We are doing everything we can to assist those who were arrested - all suspensions are hereby lifted until or whether charged, and they are welcome to return to work.
"News Corporation will cover their legal expenses. Everyone is innocent unless proven otherwise."
There had been widespread speculation that News International - the UK newspapers division of News Corp - would begin publishing a Sunday version of The Sun ever since the News of the World was closed last July over the phone-hacking scandal.
Confirming this, Mr Murdoch wrote in his memo: "We will build on The Sun's proud heritage by launching The Sun on Sunday very soon.
"Our duty is to expand one of the world's most widely-read newspapers and reach even more people than ever before."
He concluded his rallying call to Sun staff: "Having a winning paper is the best answer to our critics.
"I am even more determined to see The Sun continue to fight for its readers and its beliefs.
"I am staying with you all, in London, for the next several weeks to give you my unwavering support.
"I am confident we will get through this together and emerge stronger."
Mr Murdoch flew into the UK in his private jet last night and arrived at Wapping this morning to take charge of the crisis at The Sun.
Four protesters from the group Avaaz held a demonstration outside the main entrance to the News International building at about 12.30pm.
One wore a giant Rupert Murdoch mask and a placard reading "Hacking? Bribery? News to me".
Another wore a police uniform and carried a bag of "swag" and an "End the Murdoch Mafia" placard.
They were asked to move on to the public road by security guards.
Mr Murdoch is understood to have spent the afternoon on the newsroom floor. He is thought to have spoken to individual journalists but not made any formal address.
Staff leaving the building were reluctant to speak to waiting journalists but the mood inside was said to be "more relaxed".
Mr Murdoch spoke to a number of Sun reporters on the paper's newsroom floor accompanied by his eldest son Lachlan.
A source played down the significance of the absence of Mr Murdoch's younger son James, who is chairman of News International.
The source said: "James Murdoch has other commitments and is out of the country, and asked Lachlan to accompany his father."
PA
