Billy McAllister was fined for shouting and swearing at a man who classes himself as disabled at a bedroom tax meeting.
The 4-year-old long-standing deputy on Glasgow City Council told John Park to "f*** off" and said "You're f****** rumbled" when they both went to a meeting where Tommy Sheridan was speaking, in Ardoch Street, Possilpark, last year.
Shadow Scottish Secretary and Labour Glasgow East MP Margaret Curran has now written to Deputy First Minister Nicola Sturgeon, calling on the SNP to take action against their senior councillor.
She has been joined in her calls by Maria Fyfe, former MP for Glasgow Maryhill, where McAllister's ward is, who has questioned why "a man like this is elevated to such a senior position in their party in Scotland's largest city".
Matters could come to a head next week at the SNP group in Glasgow's AGM, where councillors were already due to elect a replacement for group leader Graeme Hendry. The Herald understands McAllister had previously expressed his desire to continue as deputy.
In her letter to Ms Sturgeon, Ms Curran said: "You will no doubt be aware of the concern amongst Glaswegians that such a man holds high office in your party and the city of Glasgow.
"I am sure you agree with me that such a verbal assault on a disabled person is completely unacceptable especially from someone holding a senior position within your party.
"I would therefore call on you as a fellow Glasgow elected member and Deputy Leader of the SNP to take immediate action to ensure that this individual is no longer allowed to hold a senior position in the SNP.
"The people of Glasgow will expect you and your party to take action in light of Cllr McAllister's conviction."
Ms Fyfe added: "What does it say about the SNP when a man like this is elevated to such a senior position in their party in Scotland's largest city?
"The SNP must take swift action against a man who has now been convicted of acting in a threatening or abusive manner."
There was no immediate comment from the SNP.
On Monday, Glasgow Sheriff Court heard McAllister was so aggressive when he shouted to Mr Park, a member of the Solidarity party, that he was "almost spitting" and had to be forcefully held back and was eventually dragged away.
Mr Park, who has metal plates in his leg and a crushed vertebrae, then went to the reception area of the Millennium centre where the meeting was held, and the police were called.
McAllister pled guilty to acting in a threatening or abusive manner and shouting, swearing and gesticulating aggressively towards Mr Park on May 29, last year. A not guilty plea to a charge of assault by pressing a key into Mr Park's face was accepted by the Crown.
McAllister was fined £200 by sheriff Lindsay Wood.