The personal diaries in which Kate McCann described her private thoughts were bought by News of the World news editor Ian Edmondson for €18,000 (£15,000), the inquiry heard.
He bought the diaries, which Mrs McCann wrote in the days following the disappearance of her daughter Madeleine in 2007, from a Portuguese journalist, the inquiry heard.
Daniel Sanderson, the reporter whose byline appeared on the story, said he wrote the article believing it would not be published unless the paper had received the explicit approval of the McCann family.
He bought a transcript of the diary from a Portuguese journalist and said in his testimony that Mr Edmondson had approved the payment of the €18,000. It was, he said, left to Mr Edmondson to get approval for publication from the McCann family. "I was told at the time that we would not be publishing the diary unless we had specific, express permission from the McCanns," he said.
Mr Sanderson added, "I have every intention of apologising to the McCanns," and said the decision to print a story based on the diaries had been wrong.
He said he had believed the authority to publish had come from the the McCann family's media spokesman, Clarence Mitchell. Mr Mitchell has stated that he gave no approval for publication and claimed his contact with Mr Edmondson had been limited to a phone call and a text message.
Colin Myler, the editor of NOTW when it published the story, told the Leveson Inquiry yesterday that when he took over from Andy Coulson in 2007 after the jailing of Glenn Mulcaire and Clive Goodman, he felt there may be "bombs under the newsroom floor" that had yet to go off.
In his testimony, which at times sounded as though he had tried to turn the tabloid into a morally upstanding version of The New York Times, he said he immediately knew practices had to be tightened. He described learning that police had removed three binliners of material from Mulcaire's home and how he felt something more would happen. "I felt there could be bombs under the newsroom floor and I didn't know where they were and I didn't know when they were going to go off," he said. He is now known to have sent an email to James Murdoch in 2008 discussing how NOTW hacking went further than Goodman or Mulcaire.
But Myler claimed a year later in a Press Complaints Commission inquiry: "Our [News International] enquiries have found no evidence of involvement by News of the World staff other than Clive Goodman in phone message interception beyond the e-mail [For Neville] which emerged in April 2008."
During one passage when Mr Myler was defending the tabloids he suggested that until the phone hacking scandal broke, the PCC had been an effective self-regulator. He was immediately rounded on by Lord Leveson who said: "Mr Myler, the PCC doesn't regulate anybody."
Piers Morgan, the former NOTW and Daily Mirror editor who is now a primetime interviewer on US television, will give evidence to the Leveson Inquiry next week.
Via videolink,he is expected to be asked about a key comment in his book, The Insider, in which a 2001 diary entry describes hacking as "a little trick" that celebrities and other public figures should be warned about.
Mr Morgan has regularly denied phone hacking was ever practised in his time at the Daily Mirror. But his book describes the technique of bypassing security barriers and tapping in a standard code to to listed to voicemail messages.
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