The proposed £363,000 budget cut sparked an outcry when it was revealed.
Council leader Adam McVey said: “Over the past week, we have heard strong views from many parents, former pupils, interest groups and other organisations, who have spoken articulately in support of keeping the City of Edinburgh Music School in its present format.
“With this in mind, we have taken the decision to remove the proposal for a Citywide Excellence and Equity Service out of the suite of proposals going forward for consultation.
“The Music School clearly has a fantastic reputation for musical excellence. We want to be sure that children of all backgrounds are given the opportunity to benefit from this and will look at alternatives proposals for doing so which will retain the current level of financial support and get the support of key stakeholders.”
Violinist Nicola Benedetti welcomed the council’s climbdown. She wrote on Facebook: “This is the only acceptable outcome to what was a shocking proposal to begin with. Young musicians need specialised support, and being around likeminded creative minds is extremely important.”