Gharibabadi made the request during a meeting with UN High Commissioner for Human Rights Michelle Bachelet in Geneva. He strongly condemned the act and urged swift action from the Human Rights Council to address the matter.
Gharibabadi emphasized that the act of desecration encourages violence, spreads hatred, and is not related to freedom of expression.
Last week, two men burned a copy of the Quran outside Stockholm's central mosque, an act that was authorized by a court.
The incident sparked widespread condemnation from the Muslim world. Gharibabadi criticized the presence of double standards within UN human rights mechanisms and called on the Human Rights Council to uphold its core mandate.
He is currently leading Iran's delegation at the 53rd session of the Human Rights Council, which is set to conclude on July 14.