A committee of MPs yesterday accused various News International executives of being behind a cover-up, and branded Murdoch "not a fit person" to run the News Corporation global empire.
The 81-year-old billionaire said that the findings of the Commons culture committee report were "hard to read", but expressed his confidence that News Corp can right the ship.
"We certainly should have acted more quickly and aggressively to uncover wrongdoing," admitted Murdoch. "We deeply regret what took place and have taken our share of responsibility for not rectifying the situation sooner."
News Corp has criticised the MPs' report, branding it "unjustified and highly partisan", particularly as the committee disagreed on the comments about Murdoch not being fit to run a company.
In his email, Murdoch said that the Management and Standards Committee (MSC), set up by News Corp to clear up the hacking affair, had found no evidence of illegal conduct at The Times and The Sunday Times beyond one previously reported incident.
This involved the hacking of a personal email address, understood to be for a story unmasking police blogger Nightjack. Murdoch noted that the employee involved had been disciplined, although the paper is currently being sued over the incident.
He also confirmed that the MSC had completed its review of The Sun, but supplied no further information on the conclusions.
"[The culture committee] report comes at a time when our business has never been stronger and we continue to demonstrate strong operational excellence focused on returning maximum value to all of our stockholders," said Murdoch.
"It is a testament to the integrity and strength of you, our more than 50,000 colleagues around the world, that we could experience such exceptional performance even in the midst of unprecedented public scrutiny. I have also never been more encouraged by your dedication and steadfast commitment to our future.
"The opportunity to emerge from this difficult period a stronger, better company has never been greater and I will look to each of you to help me ensure that News Corporation's next 60 years are more vital and successful than ever."
The culture committee's report has been overshadowed by a party political row, after the members clashed over the inclusion of statements about Murdoch.
Conservative member Louise Mensch has criticised Labour over its insistence on including the line about Murdoch being 'not fit' to run a global company, saying that the report has lost credibility because of it.
"Labour has shot themselves in the foot by taking a report that could have been quite damaging to their target and making it partisan and essentially worthless," she said on BBC Two's Newsnight.
Mensch said that the committee had never discussed "even for a minute" whether Murdoch was fit to run News Corp, but Labour's Paul Farrelly insisted that the motion was "tabled well before Easter", and widely discussed.
Labour's Tom Watson said yesterday that Murdoch was more to blame for the hacking scandal at the now defunct News of the World "than any individual alive".
The report also accused the media mogul of "wilful blindness" to alleged malpractice and wrongdoing by News Corp employees.
The committee accused ex-News International executive chairman Les Hinton, former News of the World editor Colin Myler and former legal manager Tom Crone of giving misleading evidence to parliament. However, they all deny they claims and say they stand by their evidence given to the committee.
Meanwhile, Sky has today insisted that it is "fit and proper" to hold a UK broadcasting licence, as Ofcom probes whether allegations of wrongdoing against News Corp put in doubt its ability to hold a 39.1% stake in the pay-TV giant.