News Corporation's chairman Rupert Murdoch says his company has handled the phone-hacking crisis "extremely well" and will recover.
In an interview with the Wall Street Journal, he said it would establish an independent committee to "investigate every charge of improper conduct".
Earlier he and son James agreed to appear before MPs to answer questions on the scandal on Tuesday.
The men initially declined to appear before the Commons media committee.
The Murdoch-owned News of the World (NoW) was shut down last week amid the mounting scandal over the alleged hacking of phones belonging to crime victims, politicians and celebrities.
And on Wednesday, News Corp dropped a bid to take complete control of satellite broadcaster BSkyB.
In the interview with the US paper, which is owned by News Corp, Mr Murdoch said he wanted to address "some of the things that have been said in Parliament, some of which are total lies".
He said: "We think it's important to absolutely establish our integrity in the eyes of the public... I felt that it's best just to be as transparent as possible."
But he insisted the damage to his company was "nothing that will not be recovered".
He said he acted appropriately and quickly: "When I hear something going wrong, I insist on it being put right."
Mr Murdoch also rejected criticism that James Murdoch had acted too slowly in dealing with the tabloid scandal.
"I think he acted as fast as he could, the moment he could," he said.
The second largest shareholder in News Corp told BBC Two's Newsnight that Rebekah Brooks should leave her position as News International chief executive in the event that she is shown to have been involved in phone-hacking.
Saudi Prince Al-Waleed bin Talal Alsaud, who owns 7% of News Corp, said: "You bet she has to go. Ethics to me are very important.
But he defended Rupert and James Murdoch, saying: "Speaking of my dealings with them there has been nothing but high ethics for the past 20 years."
Neil Wallis, ex-News of the World executive editor, was arrested on Thursday morning on suspicion of conspiring to intercept communications.
Mr Wallis, also a former member of the Editors' Code of Practice Committee, is the ninth person to have been arrested since the Metropolitan Police launched a fresh phone-hacking investigation in January.
In the US, it is being reported that the FBI is investigating alleged hacking of the phones of 9/11 victims by the News of the World.
A growing group of senators and a senior Republican congressman have been calling for the authorities to investigate the allegations.
Democratic Senator Robert Menendez, who wrote to the attorney general to urge an investigation, said the claims newspapers sought to "exploit information about... personal tragedies for profit" needed to be probed.
On Tuesday this week, the UK's Commons culture, media and sport committee invited the Murdochs and News International chief executive Rebekah Brooks to give evidence at the House of Commons about the phone-hacking scandal.
In a statement, the MPs said that serious questions had arisen about the evidence Mrs Brooks and Andy Coulson, both of them former News of the World editors, gave at a previous hearing in 2003.
The Murdochs agreed to give evidence after receiving summonses from the committee. Earlier in the day they had said they were unavailable to attend.
The summonses were the first to be issued by a parliamentary select committee for almost 20 years, since the sons of the late newspaper tycoon Robert Maxwell were ordered to appear in 1992.
Meanwhile, on Thursday evening, London mayor Boris Johnson met Met Police Commissioner, Sir Paul Stephenson, to discuss the hiring of Neil Wallis as a consultant for the force, for which the journalist was paid £24,000.
Home Secretary Theresa May has written to Sir Paul to get the "full picture" on the circumstances surrounding his appointment.
The Home Affairs Select Committee has also written to ask him to give further evidence on the matter next Tuesday.
As part of the contract, Mr Wallis advised the Commissioner's Office, and the Directorate of Public Affairs and Specialist Operations, working closely with Assistant Commissioner John Yates.
Meanwhile, the family of a Brazilian man shot dead by police in London in 2005 has called for the News Corp phone-hacking investigation to be widened.
In a letter to PM David Cameron, Jean Charles de Menezes' relatives say the actions of police who investigated Mr Menezes' death should be probed.
Mr Cameron has asked Lord Justice Leveson to oversee a public inquiry into the News of the World scandal and media regulation.
The inquiry will be in two parts - an investigation of wrongdoing in the press and the police, and a review of regulation in the press.