It comes as an SNP MSP said that no-one who promotes Wings Over Scotland is “fit to be an SNP member”.
The blog has been popular amongst independence supporters and many mainstream politicians since its launch in 2011.
Many high-profile SNP politicians, including Michael Russell and Jeane Freeman, promoted its contents around the 2014 referendum, including the blog’s infamous ‘wee blue book’.
Tom Arthur, the SNP MSP for Renfrewshire South, was reacting to a post by the blog, which contained an attack on The Herald’s journalist Neil Mackay.
The blog labelled the journalist an “infiltrator” and used allegedly sectarian language by highlighting the journalist’s birthplace of what was described as “ultra-Loyalist stronghold of Antrim”.
Mr Arthur posted on Twitter: "What Neil has been subjected to is utterly repulsive.”
He added: "Anyone who promotes that blog is, in my view, not fit to be an SNP member.”
Responding to the blog’s contents on Twitter, Mr Mackay called on Ms Sturgeon to “look into” the amplification of the blog by elected representatives.
He wrote: “If it is the case that this was shared or distributed or amplified by elected representatives, then I would very much like the SNP and Nicola Sturgeon as party leader to look at this please when they have the time to do so. Thank you.”
Mr Mackay had previously written: “I’ve been told SNP MPs Kenny MacAskill and Joanna Cherry were sharing and liking a hate blog which sought to attack me using a sexual offence against my daughter, sectarian dog whistles and my nationality. If true, should I presume they hadn’t read what they’re were [sic] amplifying?”
It is also understood that complaints have been submitted to the SNP in relation to the two MPs, who have been accused of promoting the blog after its publication last night.
One party source told The Scotsman: “It’s insane. The party needs to do something.”
Responding to a request for comment, an SNP source said: “Alex Salmond's supporters have got themselves in toe with some very distasteful individuals."
It is understood the subjects of the complaints include Ms Cherry, a high-profile critic of Ms Sturgeon who liked a tweet promoting the blog, and former justice secretary MacAskill, who retweeted two posts promoting the blog.
The two tweets included links to the blog and stated “Wings highlights the Pravda style manipulation of the news” and “recent polling questions on GRA reform and the Joanna Cherry sacking taken to bits by Wings Over Scotland”.
The latter tweet, from the ‘Friends of Wings’ account, was liked by Ms Cherry.
A spokesperson for Ms Cherry said “no inference” could be drawn from liking the tweet and said she was backing the statement criticising the framing of questions in a recent poll by SavantaComRes for The Scotsman.
The spokesperson said: “On Tuesday, Ms Cherry liked a tweet which criticised the framing of questions on recent polling about public attitudes towards changing the Gender Recognition Act, nothing more and no wider inference can be drawn from this.
"She has been saddened by the inclusion of unpleasant comments contained in the blog post linked in the tweet, which were directed at the journalist Neil McKay and is glad that the author of the blog post has now removed these and hopes that he will make an apology.”
Mr MacAskill and Wings Over Scotland were contacted for comment.