Iran's Culture Ministry made the decision over alleged abuse suffered by two male Iranian pilgrims traveling through Saudi's Jeddah airport in March trying to return home, the station reported.
Culture Ministry spokesman Hossein Nooshabadi told state TV that the pilgrimage would be suspended until the Saudi government "applies a strong attitude" to the case. He also said "capital punishment" should apply to the case, without offering details about it.
The alleged abuse, the details of which have not been publicly disclosed, sparked unauthorized protests at the Saudi Embassy in Tehran on Saturday. Public anger has grown over the incident, with President Hassan Rouhani ordering an investigation and Iran's Foreign Ministry summoning a Saudi diplomat over it.
"In the incident, no abuse has happened and the two policemen who attempted abuse were identified and detained by Saudi police," Ali Ghaziasgar was quoted as saying.
More From This Section
Some 500,000 Iranians visit Saudi Arabia each year for the umrah pilgrimage to Mecca and Medina, Islam's holiest sites.
Another 100,000 Iranian pilgrims annually travel to Saudi Arabia for the hajj Islam's main pilgrimage which comes after the holy month of Ramadan and is scheduled to take place in September this year. Hajj is a ritual required of every able-bodied Muslim at least once in a lifetime.
Tensions between Shiite power Iran and the Sunni kingdom of Saudi Arabia have escalated over Saudi-led airstrikes in Yemen targeting Shiite rebels known as Houthis. The US, Western countries and Sunni Arab nations involved in the Saudi-led coalition have accused Iran of supporting the Houthis militarily, something both the rebels and the Islamic Republic deny.
Shiites are considered infidels by a strict Wahhabi interpretation of Sunni Islam widely followed in the kingdom.
Politics play a part as well, especially since Iran's 1979 Islamic Revolution. Iran has insisted in the past that its pilgrims be allowed to hold "disavowal of infidels" ceremonies rallies denouncing Israel and Saudi ally the United States.
Saudi Arabia bans such demonstrations at hajj and in 1987, one such rally led to clashes with Saudi security forces in which more than 400 pilgrims, mostly Iranians, were killed. Iran stopped pilgrims from attending hajj for three years after the killings.
Iranian pilgrims still hold small-scale "disavowal of infidels" ceremonies during the hajj.