Iranian protest outside Saudi Arabia’s embassy in Tehran four days after scores of Iranian pilgrims were killed in a stampede at the hajj. (Atta Kenare/AFP/Getty Images)

Iran is demanding that Saudi Arabia, its chief rival for regional power, apologize for the stampede outside Mecca that killed at least 769 people last week.

In remarks to clerics that were published in English on his Web site on Sunday, Ayatollah Ali Khamenei, Iran’s supreme leader, said, “The Muslim world has plenty of questions in this regard and the Saudi Arabia’s rulers, instead of shifting blame [to others] must accept their responsibility in this heavy mishap by apologizing to the Islamic [world community] and their bereft families, and meeting their obligations to that effect.”

Khamenei’s remarks were the latest in a bitter exchange of accusations since the stampede during the annual hajj pilgrimage Thursday.

At least 136 Iranians died in the crush, the largest group of casualties identified, and hundreds more Iranians are missing.

Iranian officials have accused the royal family in Riyadh of criminal incompetence in managing the pilgrimage. On Saturday, Iranian President Hassan Rouhani called on the United Nations to investigate the incident. Iran has threatened to press the case against Saudi Arabia in international courts and has said that the kingdom is not capable to manage a religious rite that draws 2 million pilgrims every year.

On Saturday evening, Saudi Foreign Minister Adel al-Jubeir shot back when asked about Tehran’s criticism before he met with U.S. Secretary of State John F. Kerry.

“I believe that the Iranians should know better than to play politics with a tragedy that has befallen people who were performing their most sacred religious duty, which is the pilgrimage,” he said.

Noting that King Salman has ordered an inquiry into the stampede and a review of hajj plans for the future, Jubeir added: “We will reveal the facts when they emerge. And we will not hold anything back. If mistakes were made, who made them will be held accountable. And we will make sure that we will learn from this, and we will make sure that it doesn’t happen again.”

Saudi Arabia and Iran are religious and regional rivals for influence. Most Iranians are Shiite Muslims, while most Saudis are Sunnis.