Nicola Sturgeon’s husband, Peter Murrell, should be suspended from his job as their party’s chief executive, Kenny MacAskill has suggested.
Mr MacAskill said Mr Murrell should be investigated following the leak of WhatsApp messages appearing to show him backing police action against Alex Salmond.
The messages appear to have been sent in January 2019 after Mr Salmond had appeared in court charged with sexual offences.
It was also the month in which a separate complaint was made about the former SNP leader to the Metropolitan Police. The Met later dropped the complaint.
One message appears to show Mr Murrell calling for pressure to be put on police over Mr Salmond’s case.
A second message appears to show the SNP chief executive supporting action by prosecutors in relation to the former first minister.
The Crown Office last week instructed Police Scotland to investigate the leaked messages. One line of inquiry will be that they have come from material disclosed to Mr Salmond’s trial defence team.
Mr Salmond was cleared of all sexual offences charges at the conclusion of his criminal trial in March. His supporters have claimed he has been the victim of a plot by rival figures in the SNP.
In a blog for the pro-independence website Wings Over Scotland, Mr MacAskill said the SNP had “historically been swift” to suspend any party members when there’s “any hint” of inappropriate conduct.
“So why, then, no action against the Chief Executive?” Mr MacAskill asked.
Mr MacAskill, the East Lothian MP, suggested the messages were “purporting to encourage pressure be brought to bear on police in the Alex Salmond case”.
He added: “Indeed, they appeared even to go beyond that, with the suggestion of the instigation of another inquiry by the Metropolitan Police. (Any doubt there might have been over the document’s authenticity now resolved by the Crown instigating a police investigation into a leak.)
“Now those things may or may not be criminal but it’s certainly conduct unbecoming of a party Chief Executive, raising questions about both him and his actions. After all, the SNP is the governing party and seeking to influence criminal investigations is simply unacceptable.
“Supporting an investigation can be laudable, pressurizing those doing the investigating most certainly can’t, and the terms of reference seem clear. You’d have therefore thought action would have been swift and speedy.”
The SNP has been approached for comment.