Derry City and Strabane District Council has backed a motion calling on the cross-border language body Foras na Gaeilge to back Cultúrlann Uí Chanáin.
Under an ongoing consultation the authority is seeking views on the diversion of funding from the Great James Street centre to support new cultúrlanna around the country.
Some have suggested doing so would force Cultúrlann Uí Chanáin's closure.
The matter was raised by Sinn Féin Councillor Kevin Campbell who urged that the Derry centre's funding be maintained at its current level.
At Thursday's monthly council meeting he proposed "that Derry City and Strabane District Council notes with concern the current consultation being carried out by Foras na Gaeilge relating to funding of CultúrlannUí Chanáin. This consultation may result in the Cultúrlann losing a major portion of its funding and could, potentially, result in the building closing.
"Council acknowledges the immense contribution that the Cultúrlann has made to the promotion of the Irish language and Irish culture in Derry as well as its efforts to make the language accessible on a cross-community basis to all citizens of the city.
"We call on Foras na Gaeilge to implement Option (ii) to ensure that any future policy does not jeopardise the future of Cultúrlann Uí Chanáin."
Option (ii) would maintain An Cultúrlann's funding as it is.
His motion won cross-community support.