Although a small group of people had gathered outside Khomeini's house, the semi-official Tasnim news agency denied that the house had been set on fire. Several people can be seen cheering in the social media videos as a building catches fire in a flash.
The dates on which the videos were filmed were not independently verified by Reuters. The incident took place on Thursday night in Khomein, south of Tehran, according to activist network 1500Tasvir. Khomeini was born there.
The residence had been transformed into a museum.
"The doors of the house of the late founder of the great revolution are open to the public. The report is a lie," Tasnim said.
Khomeini passed away in 1989. Since Mahsa Amini, an Iranian Kurdish woman, died in the morality police's custody in September, his successor, Ayatollah Ali Khamenei, has come under intense pressure from nationwide protests calling for an end to hardline clerical rule.
Separate videos published by 1500Tasvir allegedly depicted protesters in a number of Sistan-Baluchistan cities, including the capital Zahedan, where demonstrators chanted "Death to Khamenei," and Chabahar, where protesters tore down and trampled the sign for an avenue named after Ayatollah Khomeini.
State media reported that authorities held a funeral service for seven people who were killed in Izeh, a city in the southwest, in what it described as a terrorist attack.
However, the mother of one of the victims, Kian Pirfalak, 10, was heard in social media videos accusing the security forces of shooting her son.
Protesters could be heard chanting "Khamenei we will bury you" in a video that appeared to be from Pirfalak's funeral and was shared on social media.
Reuters was unable to independently confirm the veracity of those videos.
On Friday, Tasnim reported pro-government demonstrators in the northeastern city of Mashhad, where two members of the Basij militia were killed on Thursday.
Aylar Haghi, a medical student who was allegedly killed by security forces during protests in the northwest Iranian city of Tabriz, was laid to rest. Videos posted on social media showed riot police confronting a crowd at the service. She allegedly died after falling into an excavation at a building site, according to the authorities.
Late on Friday, protests persisted in several Kurdish-populated towns and cities, including Piranshahr, where, in accordance with a video posted by the human rights organisation Hengaw, protesters took over a police station. Reuters was unable to confirm the footage.
According to the Revolutionary Guards' news website, two intelligence agents were killed during Thursday night's clashes with protesters.
In addition, it stated that on Thursday, one Basiji and one policeman were killed in Kurdistan, and three additional Revolutionary Guards and a Basij member were killed in Tehran.
(With inputs from Reuters)
