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.
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."
Tory leader Ruth Davidson said: "In light of these remarks, I think it would be wise for the First Minister to take a step back from the process and allow another minister to represent the Scottish Government in the proposed cross-party talks."
Willie Rennie, leader of the Scottish Liberal Democrats, added: "It is not clear to me how Mr Salmond is going to be able to convene a cross-party group of leaders to take forward the report given he has been so heavily criticised in the report."
Meanwhile an SNP spokesman said that any refusal by the other parties to "engage fully and constructively with the cross-party talks the First Minister has proposed would look silly and petulant - and would go back on the unequivocal undertakings they gave to Parliament only yesterday".