Lord Justice Leveson's report has set a testing challenge for the press and for politicians.

For the seventh time in as many decades, a report has been published which deals with concerns about the press. This time we must act, and Scotland is in a good position to get it right.

I initially thought it unfortunate when Downing Street refused to share the embargoed report with the Scottish Government on the same basis that Westminster leaders received the document. On reflection, that delay was perhaps no bad thing given that, by moving too quickly, the UK parties have got into entrenched positions.

While Westminster has split on the report recommendations, in Scotland we have the opportunity to reflect and find agreement on the way forward. A much better way to proceed is through all-party discussions to find a sensible way to implement Leveson's recommendations in Scotland that removes party political considerations.

Lord Justice Leveson's report is clear from the outset that regulation of the press is devolved in Scotland and that a different legal system applies. In setting out his recommendations, he has thrown down the gauntlet to the Scottish Parliament and it is our responsibility to act.

Leveson writes that he set out his recommendations in such a way as to enable experts in devolved jurisdictions to see how they could be made to fit. For example, any legislative underpinning of a new system will require a relationship to Scots law, particularly the civil law of defamation, whilst some of the remedies suggested in cases where press behaviour is inappropriate are not currently available in Scotland.

That is why I have proposed the establishment of an independent implementation group, chaired by a Court of Session judge, with five non-politician members. The purpose of the group would be to consider how best to implement Leveson's proposals in the context of Scots law and the devolved responsibilities of the Parliament.

On Tuesday, the Scottish Parliament will debate the report. I will lead that debate for the Government, but there will be no motion for the debate, in the hope that we can hear what the parties have to say without the usual partisan constraints.

Leveson set out clearly the difference between statutory regulation of the press on the one hand and the argument for statutory underpinning of self-regulation on the other. It is clear to me in giving evidence to the inquiry that Leveson was searching for a form of statutory underpinning that would not be considered as state regulation, in line with the Irish model of press regulation that was established four years ago.

There are differences between Leveson's proposals and the Irish model, of course, and, in some ways, it might have been better to have stuck more closely to the Irish system than to introduce the extraneous complication, in terms of the proposed role for communications watchdog Ofcom, since all the main UK titles with Irish editions have already signed up to the Irish system of regulation.

It would be impossible, for example, for the Sunday Times to argue that its UK edition is produced in an atmosphere of a free press while its Irish edition is constrained in some way. Or for the Daily Star to argue that investigative journalism is traduced in Ireland while blossoming in London.

There are a number of features of the Irish system which crystallise the value of statutory underpinning, in particular the personification of an ombudsman who can provide protection and redress for the vulnerable.

Does that mean that we should follow the Irish model exactly? No, but we should surely look seriously at whether it can be adapted sensibly to the Scottish context. And it is with this in mid that I have written to the leaders of the other parties in the Scottish Parliament inviting them to talks on the issue next Thursday.

As our response evolves across the Parliament, we must ensure it does so in a way that is tailored to Scottish conditions. While it may be true that the elements of criminality and malpractice across the media that sparked Leveson are not associated with Scottish publications, it is also true that there are victims of that potential criminality and malpractice in Scotland to whom we owe an appropriate response.

In light of the impasse at Westminster we should consider whether an independent press regulatory body – similar to the Press Council of Ireland, free from Government control but underpinned by legislation – can provide maximum benefit and the reassurance of the protection of a free press in a sensitive regulatory environment.

I believe it is clear that the case for a Scottish solution to these important and vital issues is unarguable.