Kelvin MacKenzie, the former Sun editor, has told the Leveson inquiry that News International should have been fined for 'lying' to the Press Complaints Commission about the extent of phone hacking at the News of the World.

MacKenzie, appearing before Lord Justice Leveson on Monday, made the comment after being asked how regulation of the press could be improved.

"In the end newspapers are commercial animals; they try to make money... I would be in favour of fines – and heavy fines for newspapers that don't disclose the truth to the Press Complaints Commission," he responded.

MacKenzie gave as an example the PCC's November 2009 report on the Guardian's revelation that phone hacking at the News of the World was more widespread than a single rogue reporter, the line that publisher News International stuck to until late 2010. At the time the PCC report found no evidence that it was "materially misled" by the News of the World over alleged phone hacking.

"They [the PCC] were lied to by News International and they should pay a commercial penalty for that," said MacKenzie.

He added: "I think the threat of financial penalty will have a straightforward effect on newspapers … no editor, no proprietor would dream of lying under those circumstances."

News International subsequently admitted that the practice was more widespread and has paid compensation to a number of individuals who were victims of phone hacking.

At the height of the phone-hacking scandal in July last year the PCC admitted that subsequent events "self-evidently undermined assurances given to the PCC by News International in the past" and it could no longer stand by the November 2009 report.

MacKenzie disputed evidence given to the inquiry last year by Anne Diamond about her dealings with the Sun over its publication when he was editor of a front-page picture of the funeral of her infant son.

He denied that the paper had used emotional blackmail to get Diamond to support a Sun campaign for a cot death charity.

MacKenzie said the day after the front-page picture was published two of his senior Sun executives went to Birmingham to meet Diamond and her husband to discuss the paper's coverage of her son's death and the cot death campaign.

He added that if she felt so strongly about the paper's coverage of her son's funeral, the following day "presumably she would never have sat down with Sun executives and agreed to set up a charity".

"I have met her on two or three occasions since then and she has never said she was forced into doing anything," he added. "If she felt as strongly as she appeared to feel at Leveson you would have thought 20 years earlier she would have been massively hostile to us, and she wasn't."

MacKenzie denied Diamond's claim that News International proprietor Rupert Murdoch had instructed his editors to target her after she confronted him at a social event. "I've never heard him say 'go after somebody' in any circumstances – whether it's the prime minister or a fading breakfast show host," he said.

He also said he could not recall receiving a letter from Diamond 20 years ago "begging [him] to stay away" from her son's funeral, or conversations from that time about the issue.

When pressed on the matter by the inquiry counsel, Robert Jay QC, MacKenzie, growing visibly angry, replied that Diamond was a "devalued witness" and the Sun's cot death campaign had raised £250,000 over a period of five years or more. "Why should everyone accept what she says and not accept my version of events?"

MacKenzie was also asked about the fallout from the £1m libel payout to Elton John for an inaccurate front-page story during his editorship and Sun proprietor Rupert Murdoch's reaction.

"I remember sending him [Murdoch] a fax [with details of the legal settlement] … If that went at 1.01, the phone then rang at 1.01 and 40 seconds and i then received 40 minutes of non-stop abuse," he said. "It wasn't just the money, it was the shadow it cast over the paper."

The idea that Murdoch would take setbacks such as the Elton John libel payout "on the chin" was "preposterous", according to MacKenzie.

He was also asked if Murdoch had thought he had gone too far as editor with things such as the Elton John story. "He felt we might lose too many friends," MacKenzie replied.

He added that when he was editor the Sun was much more important, relatively speaking, to Murdoch's global media empire and they would speak almost daily and the proprietor would have a "general view about the general feel of the paper, whether it was upbeat enough", but would not involve himself so much in the detail of every story.

MacKenzie also told the inquiry he believed different standards were applied to different papers when it came to judging the ethics and legality of stories and whether they were in the public interest, which he put down to snobbery.

"If you publish it in the Sun you get six months, if you publish it in the Guardian you get a Pulitzer prize," he said.

When asked to expand on this comment by Leveson, MacKenzie added: "People view the Sun at the bottom of the pile and for as long as it exists I think they view papers like the Guardian as the top of the pile."

He said the Sun "would have come very very very close to being shut down" if that newspaper had "got the Milly Dowler story wrong", referring to the Guardian correction before Christmas on deletions of the murdered teenager's voicemail messages.

Leveson replied: "It's an interesting assertion that the Guardian got the Milly Dowler story completely wrong."

MacKenzie was also questioned directly by Leveson about the importance of checking facts prior to publication.

He agreed that this was important, but added: "Both law and journalism are in the uncertainty business." "There is no absolute truth in any newspaper and there is no absolute truth in any court," he said.

MacKenzie also said time constraints were a factor in checking the accuracy of stories before publication and it is "very very hard to be 100% accurate".

"Journalists try to get things right. People tell you lies. People think it's the truth … it is a massively difficult problem particularly being a print journalist today," MacKenzie said.

Leveson replied that he recognised time constraints meant mistakes may be made, but added "that's not an excuse for not having a go".

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