"Any threat against the supreme leader is waging war on God, which carries a death sentence," Ahmad Khatami, a member of Iran's Assembly of Experts, said in a speech in Tehran.
Omid Sarlak was found dead in a car in western Iran on Saturday, shortly after posting a video of himself burning a photo of Khamenei. Police called it a suicide, but his family said he was killed by the state.
Mourners in city of Aligoudarz on Monday chanted slogans against Khamenei during Omid’s funeral.
In recent days, some ultra-conservative figures in Iran have called for tough sentences to curb social unrest.
"The sentence for someone who rejects the hijab is execution. If the martyrs were here today, they would skin alive those who stripped themselves bare with the slogan 'Woman, Life, Freedom,'" Hassan Hassannia, a former Islamic Revolutionary Guard Corps (IRGC) commander, said on Saturday.
Islamic Penal Code provisions for insulting the Islamic Republic's leader prescribe six months to two years in prison.
In the latest example of such imprisonment sentences, Forough Khosravi, a primary school teacher from Behbahan, was sentenced to 15 years in prison by the city's Revolutionary Court.
Two years of her sentence were for "insulting the leader" and two years for "insulting the founder of the Islamic Republic."