Culture Secretary John Whittingdale has revealed his faith in press freedom was "tested to the utmost" by a string revelations about his private life.
But he has maintained that politicans must "tread very carefully" when it comes to press regulation.
Last week four national newspapers were accused of being involved in a cover-up when they decided not to report on Whittingdale's past relationship with a woman who worked in the sex industry.
Since then the Mail on Sunday has reported on two further ex-girlfriends of the minister – a former Page 3 girl and a "mysterious beauty from Belarussia".
The Evening Standard this week published a front-page story about Whittingdale making an official visit to a lapdancing club.
He told MPs during culture questions: "Having had my faith perhaps tested to the utmost I still believe that press freedom is a vitally important component of a free society and we should tread very carefully.
"However the recommendations of the Leveson report have, some, already been implemented and the system is coming in today.
"But the exemplary damages provisions of section 40, you will be aware, have been enacted now, the remainder are still under consideration but we do not yet have a recognised press regulator in place but we will continue to consider these matters very carefully."
Under Section 40 of the Crime and Courts Act, publishers who are members of an officially-recognised regulator (under the Royal Charter) are protected from paying exemplary damages in libel and privacy cases.
Most UK national and regional newspapers have rejected the Royal Charter system and have instead signed up to their own regulator, IPSO.
Whilst exemplary damages are extremely rare, publishers were highly concerned about another part of Section 40 which said those outside the Royal Charter system would pay both sides' costs even if they won libel and privacy cases.
Last October Whittingdale said he was not minded to enact that provision and that appears to remain the case.
Shadow culture secretary Maria Eagle said: "I'm starting to realise why this department is known as the ministry for fun.
"We all know Mr Whittingdale's been distracted from doing his job as Culture Secretary lately by his extra-curricular activities.
"I'm talking about his moonlighting for the Leave Campaign."
She later referred to a letter that had "fallen in to my lap".
Labour's Paul Farrelly criticised the Culture Secretary for "breaking promises" by failing to push forward with parts of press regulation reform, including cost provision for victims.
The Newcastle-under-Lyme MP said: "Can I thank you for taking us no further forward?
"Implementation of these cost incentives was promised by the then culture secretary Maria Miller, they were promised as a key part of the Leveson reforms specifically by the Prime Minister, not only to Parliament but also to the victims of press abuse, including the family of Madeleine McCann.
"So in signalling already that he has no intention of taking this step, have you reflected very much at all that it is not only thwarting the will of Parliament, breaching a cross-party agreement but also breaking very firm, clear and unequivocal promises made by the Prime Minister and his colleagues?"
Whittingdale said: "I have not indicated that I have no intention, I simply said I was not minded, which means that the matter is still under consideration and my mind and that of my colleagues is open on the matter. Which is why we are continuing to have meetings."
He also added that cost provision for victims could not come into effect until there is a "recognised regulator".
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