The motion also asks council to endorse leading international studies which concluded that the practice is unethical and harmful.
Councillor McCauley said: “Prior to bringing this motion before the council I have had extensive talks with the local LGBT community on this issue. I am pleased that I have got the full support of the Rainbow Project, Cara-Friend and Foyle Pride.
“There is nothing wrong with being gay, lesbian, bisexual or transgender and Sinn Féin is totally opposed to the use of ‘therapies’ which are aimed to change, repress and, or eliminate a person’s sexual orientation, gender identity and, or gender expression.
“These ‘therapies’ are damaging, extremely dangerous and can have a very damaging psychological effect on people.
“The practice of conversion therapy has been condemned and discredited worldwide by institutions such as the UN Committee Against Torture, the European Parliament and by the Irish Council for Psychotherapy.
“We believe that ‘conversion therapies’ should be a banned throughout Britain and Ireland,” he added.