An Iranian delegation has left Saudi Arabia without an agreement for its citizens to attend the Muslim hajj pilgrimage this year, Saudi media have reported, a second failure by the rival Middle East powers to strike a deal.

Relations between the two countries plummeted after hundreds of Iranians died in a crush during last year's hajj and after Riyadh broke diplomatic ties when its Tehran embassy was stormed in January over the Saudi execution of a Shiite cleric.

The dispute has provided another arena for discord between the conservative Sunni Muslim monarchy of Saudi Arabia and the revolutionary Shiite republic of Iran, which back opposing sides in Syria and other conflicts across the region.