Huntington's Disease is a genetic disorder which affects memory, judgment and muscle coordination.
Campaigner Annie McKenzie, who runs the Live for Life Foundation, which was set up to highlight the disease for which there is no cure, was at the City Chambers to hear SNP Greater Pollok councillor David McDonald, ask the council to support a motion calling for an action plan to raise awareness of the condition.
He said: "Huntington's affects around 1000 thousand families in Scotland.
"It is a hereditary condition and a child with a parent with Huntington's know they have a 50% chance of inheriting the gene.
"I hope we can create a centre of excellence to ensure all those families living with the condition can also live with hope in the knowledge the city supports them."
Mr McDonald was supported by Bill Butler, the Labour councillor for Greater Pollok.
He said: "I am only just beginning to find out about Huntington's Disease. We all need to find out more about the way we can support sufferers and their families."
The council agreed to support the motion to work with Greater Glasgow and Clyde Health Board to raise public awareness of the condition.