The Scottish Defence League (SDL) had proposed its members and supporters would march from St Giles’ Cathedral to the Grassmarket later this year.
However, the city council has now told the SDL to submit an alternative route before a decision on whether to permit the demonstration on Saturday, May 26 is taken.
The SDL describes itself as standing against the rise of Islamic extremism, but opponents of the group believe its views to be racist.
Conservative councillor for the Old Town and licensing committee member Joanna Mowat told the Evening News: “I don’t think it’s reasonable for the SDL to hold a rally in the Grassmarket where they will be surrounded by residential properties.
“The committee did not make a decision about whether the march was OK to go ahead, we just said we did not think the route was suitable.”
An application for an Orange march through Gorgie on the same day has been submitted by the Apprentice Boys of Derry.
Last September, the SDL staged a demonstration at Waterloo Place after being refused permission to march.
The group has now said if permission for its latest march is not granted, it will hold a static demonstration at the Grassmarket on that date and on a monthly basis in the city from there on.
Regional organiser Graham Walker said: “The Apprentice Boys of Derry are wanting to march through Gorgie – which is residential – but the council has told us to find another route because there’s people living in the Grassmarket?
“We will keep coming back and it will cost the council thousands of pounds, because it just seems like there is one rule for one group and one rule for another.”
Mr Walker added that if the council banned the march the group would attempt to overrule the decision in the appeal courts.
“I don’t think any judge in their right mind would look at our track record and think we had done anything wrong.”
Responding to the SDL’s threats, Councillor Mowat said: “It appears the SDL are trying to pressurise us. It will be interesting to see whether they choose to be reasonable or whether they choose to go their own way.”
A council spokesman said: “The application has been continued to the next licensing committee for the organisers, council and police to consider alternative routes.”
The matter will be considered again on April 20.