Iran’s Supreme Leader Ayatollah Ali Khamenei has again criticised Saudi Arabia over its management of hajj, after hundreds of pilgrims were crushed to death last year, and suggested Muslim countries should think about ending Riyadh’s control of the annual pilgrimage.

“Because of these (Saudi) rulers’ oppressive behaviour towards God’s guests (pilgrims), the world of Islam must fundamentally reconsider the management of the two holy places and the issue of hajj,” Khamenei said in a message carried by his website and Iran’s state media.

Saudi Arabia in turn accused Iran, its arch rival in the region, of seeking to politicise this month’s event, when millions of faithful descend on Mecca, saying Iran was compromising safety with its actions.

“The Iranian authorities are the ones who do not want the Iranian pilgrims to come here for reasons concerning the Iranians themselves and in light of them seeking to politicise hajj and turn it into rituals against Islam’s teachings and that compromise the safety of hajj,” the Saudi Press Agency quoted the kingdom’s Crown Prince Mohammed bin Nayef as saying.

Saudi Arabia is home to Islam’s most revered places, Mecca and Medina, and the government organises hajj for Muslims around the globe. Hajj is one of the five pillars of Islam, which every able-bodied Muslim who can afford to is obliged to undertake at least once in his or her lifetime.

Riyadh said 769 pilgrims were killed in the 2015 disaster, the highest hajj death toll since a stampede in 1990. Counts of fatalities by countries that repatriated bodies showed that more than 2,000 people may have died in the crush, more than 400 of them Iranians, according to news agency Reuters.

Iran blamed the 2015 disaster on the organisers’ incompetence. Pilgrims from the Islamic Republic will be unable to attend hajj, which starts on 11 September this year, after talks between the two countries on arrangements broke down in May.

“What Iranian media and some Iranian officials are raising is not objective and they know before anyone else that the kingdom has given the Iranian pilgrims what it gave others,” Crown Prince Mohammed bin Nayef said.

An official Saudi inquiry into the tragedy has yet to be published, but authorities suggested at the time that some pilgrims had ignored crowd control rules.