Media reported at least 14 others suffered injuries in the explosion at the eight-storey building, which blew out windows and covered the street below in debris.
Khamenei referred to the nationwide protests as "a coup," hardening the government's position as tens of thousands of people reportedly have been detained since the start of the demonstrations.
The US-based Human Rights Activists News Agency (HRANA) said it has confirmed 6,479 people were killed in the protests, as internet restrictions imposed on January 8 continue to slow verification.
The listing came after the 27-nation bloc sanctioned 15 Iranian officials, including top commanders in its Revolutionary Guard, over the violent crackdown on protesters.
In his latest post on Truth Social, Trump did not mention the protests but said Iran needed to negotiate a deal over its nuclear programme, which the West believes is aimed at making an atomic bomb.
