But Bill Butler insists other groups must continue to be allowed to meet in George Square, even after its £15million facelift.
The Labour councillor for Greater Pollok, who is a former MSP, made the call at a council meeting to discuss a review of policies governing public processions.
Since new controls were introduced a year ago, the number of marches through the city has fallen from 497 two years ago to 362 this year – a drop of more than 27%. The cost of policing the events is down more than £250,000.
Widespread consultation was held into how the policy was working and into a number of planned changes.
One was that groups organising large marches should not be allowed to use George Square as an assembly or dispersal point.
But a report to councillors said: "There was almost universal disagreement with the suggestions. Various respondents cited the historic and cultural significance of George Square in the history and civic life of the city as a place of protest and assembly."
George Square can't be used for the next two years because upgrading work will be carried out. As a result, councillors decided to defer a decision and hold further discussions with groups that use the civic heart of the city.
Mr Butler said: "I am delighted there is no objection to George Square being used because that would be completely wrong. There cannot be a situation where George Square becomes a 'no go' area for assembly to march off.
"George Square is a historic location for democratic assembly and post-Olympics there were 20,000 people in the square.
"I would never like to see a situation where something like that was prohibited."
But Mr Butler insisted far right wing groups should be banned from meeting in the city.
He asked: "What can we do as a council to prevent racist, fascist organisations spreading alarm among the public, intimidating people going about their normal business and spreading their obscene Nazi ideology, which is inciting racial hatred?"
Annemarie O'Donnell, executive director of corporate services, said a raft of legislation covers the control of public meetings.
She said: "We are limited in how we can assess applications. It is a very challenging area."
Councillors were told requests from extreme right wing groups to hold a march or meeting have to be treated in the same way as any other organisation.
Ms O'Donnell said: "If organisations stay within the terms of the legislation it is difficult to prevent them."
But Mr Butler insisted: "All we can do to prevent them we should do, but it is not going to be easy."