A post from the Twitter account of an SNP MSP which suggested Jacob Rees-Mogg will "undoubtedly rot in hell" has been reported to the Ethical Standards Commissioner.
James Dornan, who represents Glasgow Cathcart, was reportedly replying to the Conservative MP's post about the Nationality and Borders Bill.
Mr Dornan's account can now only be seen by those following him.
The SNP said: "It is essential such callous policies are called out."
Mr Rees-Mogg had quote-tweeted a video from the Commons Leader account, adding: "The bands of blighters bringing illegal entrants to Blighty will be broken up by this brilliant borders bill."
The reply from Mr Dornan's account read: "Hope you remember this the next time you go to confession.
"You and your cronies are already responsible for the deaths of thousands and you're now happy to see the most desperate people in the world suffer and drown.
"If your god exists you will undoubtedly rot in hell."
Mr Dornan's account has since been protected, meaning only the people following him can see any posts made.
'Poisonous and beyond the pale'
Scottish Conservative chief whip Stephen Kerr MSP criticised his Holyrood colleague and called for an immediate apology.
Mr Kerr said: "These comments from James Dornan were poisonous and beyond the pale.
"He is well known for his outbursts on Twitter but this vitriol simply has no place in respectful political debate.
"This gaffe-prone MSP has once again shown his nasty side and shamefully brought religion into his anger at a fellow elected representative."
He added: "It is clear that he wasn't interested in adhering to the MSPs' Code of Conduct when posting this reply, which is why this post has now been reported to the Standards Commissioner.
"James Dornan must urgently apologise for this wholly unacceptable and abusive behaviour immediately."
An SNP spokesman said: "The Scottish Tories' desperation to pass judgment on a tweet while utterly failing to condemn the immigration regime of their bosses in the Westminster government speaks volumes.
"While some people appear determined to be offended regardless of what SNP politicians say, there are fewer things more offensive than a policy which threatens to jail desperate refugees for the crime of trying to save their own lives - and the lives of their infant children - and it is essential such callous policies are called out."
The Ethical Standards Commissioner, which investigates complaints about the behaviour of MSPs, has been contacted for comment.