Billy McAllister, 60, told John Park to "**** off" when they went to a meeting where Tommy Sheridan was speaking, in Ardoch Street, Possilpark last year.
The city council's SNP deputy leader said to be was so aggressive when he shouted to Mr Park he was "almost spitting" and had to be forcefully held back and was eventually dragged away.
A shaken Mr Park - a member of the Solidarity party - then went to the reception area of the Millennium Centre where the meeting was, and police were called.
At Glasgow Sheriff Court yesterday McAllister pleaded 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.
Mr Park had gone to the meeting with Mr Sheridan and said he had gone outside for a cigarette when Mr McAllister shouted at him.
It was said on behalf of McAllister that Mr Park allegedly made a comment about his brother who committed suicide.
McAllister, who represents Canal ward, was elected to Glasgow City Council in 2006 after vowing to evict the Lyons crime gang from Chirnsyde, a taxpayer-funded community centre in Milton.
Crime boss Eddie Lyons ran the centre despite repeated warnings about his family's drug dealing and violence.
It closed after a feud between the Lyons and Daniel families led to the murders of Eddie's nephew, Michael Lyons and Daniel enforcer Kevin "Gerbil" Carroll.
McAllister suffered death threats during the campaign, which led to the centre's return to the community.