American pastor Terry Jones had earlier threatened to burn copies of the Quran on the ninth anniversary of the Sep 11, 2001, attacks. He later relented.
However, a group tore up pages of the holy book in a protest outside the White House on Saturday, Sep 11.
"From the point of view of Islamic jurisprudence, strong objection to such thoughts is mandatory and necessary and killing the people who have committed this act is compulsory," News.com.au quoted Hossein Nouri Hamedani, as saying.
Hamedani's view was echoed by Naser Makarem Shirazi, who said that action must be taken after consulting a "religious judge".
"The blood of the person who burns the Koran can undoubtedly be shed. But in this issue, no action should be taken without the permission of a religious judge," Shirazi said.
Meanwhile, around 500 people demonstrated outside the Swiss embassy in Tehran in protest against the Quran-burning issue in the United States.
Several protesters, carrying copies of the Quran on their heads, set US and Israeli flags on fire, and chanted, "Death to America! Death to Israel!"
The Swiss embassy manages US interests in Iran since Washington and Tehran have had no diplomatic ties since the 1979 Islamic revolution.