The News Corporation boss announced the replacement publication for The News of the World during crisis talks at The Sun offices over the paper's future in London's News International compound today (February 17), arranged following the arrest of ten current and former senior staff for alleged corrupt payments to public officials.
In an email to staff, he wrote: "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. Having a winning paper is the best answer to our critics."
Murdoch added that he has lifted all staff suspensions pending police inquiries and would offer his "unwavering support" to those who have been arrested.
"I remain grateful for your superb work and for the stories you uncover to inform and protect the public," he said. "My continuing respect makes this situation a source of great pain for me, as I know it is for each of you. We will obey the law.
"Illegal activities simply cannot and will not be tolerated - at any of our publications. Our board of directors, our management team and I take these issues very seriously."
"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."
The Sun on Sunday had been tipped to launch in April, but was allegedly put on hold following the arrests.
It has long been rumoured to fill the void left by The News of the World, which was axed in July when illegal phone hacking activites at the publication were unearthed.
The announcement comes after several senior Sun journalists planned to mount a human rights challenge to the independent Management Standards Committee over investigations at the paper.
Murdoch said today that he will continue to "turn over every piece of evidence" to the MSC, which has been instructed to co-operate with police.
He said that they will comply "not just because we are obligated to but because it is the right thing to do".