Members of Gaelic parents group Comann nam Prant do not want their children to be moved from James Gillespie's, which currently provides the city's Gaelic Medium Education (GME) at secondary level, into Tynecastle High.
Education bosses are proposing the move due to capacity pressures at Gillespie's, which they believe will worsen in coming years due to the increasing popularity of Gaelic.
Comann nam Prant has suggested that rather than moving the pupils to Tynecastle, which is currently only two thirds full, the catchment area for Gillespie's should be reviewed as there are "several neighbouring secondary schools with spare capacity".
In a letter to city education leader Councillor Marilyne MacLaren, Alasdair Cameron, convener of Comann nam Prant, said: "The Gaelic Act (2005) seeks to ensure that Gaelic is accorded 'equal respect' to English.
"While City of Edinburgh Council may have concerns over possible capacity issues at a fairly distant future, the presumption that GME children should be the ones who are required to move and lose all the educational investment does not demonstrate equal respect for Gaelic.
"It is unjust and disrespectful for pupils in GME to be placed in this position of instability and uncertainty.
"No other group of pupils in the city is discriminated against in this way.
"An alternative and far more cost-effective option would be to address the issue by changing the catchment boundaries for James Gillespie's."
Education bosses say that an "accommodation pressure point" will be reached at Gillespie's in 2016 but argue that an earlier move would "allow a more gradual transition to a naturally growing and developing Gaelic language provision at Tynecastle".
They also say that because half the pupils at Gillespie's will be decanted to a makeshift school in January 2013 while the school is rebuilt, an earlier move would avoid "unnecessary additional upheaval for future Gaelic S1 intakes".
Gillian Tee, director of education, also believes changing the Gillespie's catchment area would be "inappropriate" as it would "move local pupils from their local school".
Ann Henderson, chair of the parent council at Gillespie's, said the school did not want to lose the GME unit and that the preferred option would be to increase the capacity of Gillespie's when it is rebuilt.
She said: "We want to see the Gaelic provision remaining at Gillespie's because we feel it is part of the mix and culture of our school."Behind the scenes, I think the issue here is trying to fill up Tynecastle."
Cllr Marilyne MacLaren said: "It's undeniable that we cannot build the school any bigger. This means options are limited to Tynecastle or to moving feeder primary school pupils to another secondary, and I don't think the latter can work."