The advertisements will run in every national newspaper in the UK this weekend, including the Financial Times.
The statement comes just a day after Mr Murdoch told the Wall Street Journal that News International had made only “minor mistakes” in his handling of the crisis.
On Friday several MPs, including Ed Miliband, leader of the opposition, and Labour campaigners on phone hacking including Lord Prescott, Tom Watson and Chris Bryant, sharpened their criticism of the Murdoch family’s handling of the crisis. Rupert Murdoch and his son James will appear before MPs on Tuesday.
Rebekah Brooks, chief executive of News International, resigned on Friday after a week of pressure that has already seen the closure of the News of the World, the Murdochs’ biggest-selling UK newspaper, and the withdrawal of News Corp’s planned bid to take full control of British Sky Broadcasting.
But Mr Murdoch will say that News International will take “further concrete steps” to resolve the scandal created by allegations of phone hacking across its newspapers.
“Our business was founded on the idea that a free and open press should be a positive force in society. We need to live up to this,” he writes. “In the coming days, as we take further concrete steps to resolve these issues and make amends for the damage they have caused, you will hear more from us.”
The News Corp chairman promised more initiatives in the coming days to tackle the damage caused by the phone hacking scandal.