Labour councillor Peter Gruen made the comments following an incident where a 23-year-old woman, who has Down's Syndrome, was verbally abused by yobs near the Co-op supermarket in Swarcliffe.
Her mother, Karen Horner, has launched an appeal for information and started a Facebook group, called Keeping Swarcliffe Safe, to try to tackle anti-social behaviour in the area.
Coun Gruen, who represents Cross Gates and Whinmoor, said that outreach youth workers are aware of 'hotspots' of anti-social behaviour in Swarcliffe and Whinmoor and are working with police to catch those responsible.
He said: "I was absolutely horrified to hear about this incident, it is completely unacceptable.
"I have been in touch with the police, who have visited the house and the family are assured that this is not something being ignored.
"The council, police and youth workers are aware and are keeping an eye on this area.”
Coun Gruen said that action has been taken and some individuals responsible for anti-social behaviour have been identified.
-> The worst streets for crime in Leeds city centre - revealed by policeHe said that in some cases the police have visited the homes of those individuals and are working with their families to try to curb the problem.
West Yorkshire Police are aware of incidents in the Swarcliffe Avenue area and urge anyone with information to contact them on 101.
In a statement, they said: "Police in Leeds have recorded a harassment related hate crime in relation to incidents outside shops in the Swarcliffe Avenue area between April and June 26 this year in which a 23-year-old woman was the subject of verbal abuse by a group of youths.
"All reports of hate crime and hate incidents are taken very seriously and we always encourage victims to come forwards.
"Officers have been speaking with the victim as enquiries progress."