Labour has called for the First Minister to stand aside and let his deputy head an inquiry into how Lord Justice Leveson's report into press standards could be implemented in Scotland.
The party said the process would have "more credibility" if Deputy First Minister Nicola Sturgeon or a senior member of the Government took charge instead of Alex Salmond.
The call came after Lord Justice Leveson found that Mr Salmond would have knowingly led UK ministers to break the law if it advanced Scottish interests.
The First Minister displayed a "striking" readiness to lobby UK Business Secretary Vince Cable and former culture secretary Jeremy Hunt on behalf of Rupert Murdoch's News Corp during their consideration of the legality of its proposed acquisition of BSkyB, according to the Inquiry Report released on Thursday.
However, Lord Justice Leveson found no evidence of a deal to trade News Corp newspaper support for the SNP in exchange for Scottish Government support for the BSkyB bid, but he noted that both were discussed during the same conversation.
Ultimately, Mr Salmond did not contact the UK ministers, despite indicating his willingness to do so, and therefore "cannot be criticised" because he must be "judged by what he did, as opposed to what he said he was prepared to do".
Earlier this week, Mr Salmond proposed that an independent group should look at how best to implement the findings of the Leveson report north of the border. The First Minister said he wanted to achieve cross-party agreement on what needed to be done in the wake of it.
Responding to the report's findings, Labour MSP Patricia Ferguson, the party's culture spokeswoman, told BBC Radio Scotland: "We think that Mr Salmond's judgment in this entire scenario has been flawed and we think therefore that he should stand aside from this and allow either his deputy or another senior member of his government to take over the task."
Ms Ferguson also denied suggestions she was seeking to score political points, saying on the Good Morning Scotland programme: "It's very much not about that. We want to see press regulation that is fair, that is just and that works well in Scotland."
However, Culture Secretary Fiona Hyslop told the BBC that Mr Salmond should "of course" be involved in the post-Leveson process, adding: "It's really important that the opposition parties rise to their responsibilities, put their petty party politicking to one side and remember that quite clearly in the report, Lord (Justice) Leveson said that Alex Salmond could not be criticised and recognised that his motivation was for jobs for Scotland."