(CNN) Three days after hundreds of people died in a stampede at the holiest Muslim pilgrimage, the Hajj, Iran's Supreme Leader lashed out at host nation Saudi Arabia.

"Saudi rulers, instead of shunning (responsibility), must accept their responsibility in this grave incident by apologizing to the Muslim Ummah and bereft families," said Iranian Supreme Leader Ayatollah Ali Khamenei on Sunday, according to Iranian state-run Press TV.

At least 769 people were killed in a stampede in Mecca, Saudi Arabia, on Thursday, according to Saudi state-run SPA news agency. At least 934 people were injured.

Whereas many other nations have so far reacted to the tragedy with a more diplomatic and conciliatory tone, Iran, a bitter rival, has blasted Saudi Arabia.

Iranian President Hassan Rouhani cut short his visit to the United Nations and is expected to return home Monday to participate in a ceremony marking the return of the bodies of those Iranian who lost their lives in the stampede, the state-run IRNA news agency reported.

"This is not a situation with which to play politics," Saudi Foreign Minister Adel al-Jubeir said Saturday. "I would hope that the Iranian leaders would be more sensible and more thoughtful with regards to those who perished in this tragedy and wait until we see the results of the investigation."

Possible causes

Photos: The Hajj: Muslims gather for annual pilgrimage Photos: The Hajj: Muslims gather for annual pilgrimage Muslim pilgrims make their way to cast stones at a pillar in the "stoning the devil" ritual Thursday, September 24, in Mina near Mecca, Saudi Arabia. At some point during this last rite of the annual Hajj, a stampede occurred, killing and injuring hundreds . More than 2 million Muslims have been making the pilgrimage to the holy city of Mecca. The Hajj is one of the most celebrated events in the Islamic calendar. Hide Caption 1 of 8 Photos: The Hajj: Muslims gather for annual pilgrimage A pilgrim reads the Quran on a rocky hill called the Mountain of Mercy, on the plain of Arafat, near Mecca on Wednesday, September 23. Hide Caption 2 of 8 Photos: The Hajj: Muslims gather for annual pilgrimage Muslim pilgrims pray at Namira Mosque on September 23 on Mount Arafat near Mecca. Hide Caption 3 of 8 Photos: The Hajj: Muslims gather for annual pilgrimage Pilgrims join in one of the Hajj rituals early September 23 on Mount Arafat. For most Muslims, the pilgrimage is the spiritual climax of their lives, with many saving for decades to be able to make the journey to Mecca. Hide Caption 4 of 8 Photos: The Hajj: Muslims gather for annual pilgrimage Muslim pilgrims pray on the Mountain of Mercy, on the plain of Arafat. Islam requires every Muslim who is physically and financially able to make the journey to Mecca at least once in his or her lifetime. Hide Caption 5 of 8 Photos: The Hajj: Muslims gather for annual pilgrimage Muslim pilgrims pray on the Mountain of Mercy on Tuesday, September 22. Hide Caption 6 of 8 Photos: The Hajj: Muslims gather for annual pilgrimage Muslim pilgrims touch Islam's holiest shrine, the Kaaba , at the Grand Mosque in Mecca on Monday, September 21. Performing the Hajj is one of the five pillars of Islam. Hide Caption 7 of 8 Photos: The Hajj: Muslims gather for annual pilgrimage Muslim pilgrims circle counterclockwise the Kaaba at the Grand Mosque in Mecca on Monday. The pilgrimage, conducted over five days, includes detailed rituals including wearing a special garment that symbolizes human equality and unity before God, a procession around the Kaaba and the symbolic stoning of evil. Hide Caption 8 of 8

Saudi officials have said that they're investigating what caused hundreds of pilgrims to get trampled.

Among the suggested causes: rushing to complete the rituals, extreme heat, throngs of worshippers pushing against one another in opposite directions, even confusion among the many first-timers on the annual Islamic pilgrimage.

On Saturday, Saudi Arabia categorically denied "misleading and distorted allegations" about road closures that it believes started through Iranian state-controlled media.

"Claims that the stampede occurred following road closures because of a ministerial event or a dignitaries convoy are false," said Prince Mohammed bin Nawaf Al Saud, Saudi ambassador to the United Kingdom and Ireland, in a statement.

And Hezbollah leader Hassan Nasrallah told Lebanese al-Manar TV that Saudi Arabia should let the management of the pilgrimage be a joint Muslim issue or allow a Muslim committee to supervise its management.

Here's the latest on what we know:

Victims from many lands

More than 2 million people from around the world arrived in Saudi Arabia for last week's Hajj, a pilgrimage that all Muslims who are physically and financially capable must make at some point in their lives.

And the 769 who died came from more than a dozen countries.

At least 169 Iranian pilgrims died; 298 are unaccounted for, according to official Iranian news agency IRNA.

Indonesia reported 41 of its citizens dead, 10 injured and 82 unaccounted for.

India reported 45 of its citizens died. Egypt counted 55 among the dead. Pakistan reported 36 deaths; Cameroon, 21; Somalia, eight; Algeria, seven; and Senegal and Kenya reported five each.

Nigeria and Morocco each reported three deaths; Turkey, two; and the Philippines and the Netherlands each reported one.

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And there's more anxiety from loved ones.

The Muslim Council of Wales said it had heard from only two of six tour groups that had traveled from south Wales for the Hajj. Together, the groups number about 250 pilgrims, council official Saleem Kidwai said.

He said families are "very anxious, very concerned."

Too many people, too little time

The millions of pilgrims must perform a litany of rituals in five days, including the symbolic stoning of the devil in the neighborhood of Mina, just two miles from the Mecca holy site.

That's where the deadly stampede took place Thursday, the third day of the five-day event.

Hajj pilgrim Ethar El-Katatney, a journalist and blogger, said the pressure to finish in time may have contributed to the stampede.

"There's so little time to complete the rituals," she said.

On top of that, worshippers were trying to push their way in opposite directions -- some headed to the site of the stoning, some coming back from their previous ritual.

"Heavy pushing ensued," pilgrim Ahmed Mohammed Amer said. "I'm at a loss of words to describe what happened. This massive pushing is what caused the high number of casualties among the pilgrims."

Extreme heat and exhaustion

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The journey is physically grueling enough on its own.

But with temperatures soaring over 43 degrees Celsius (110 degrees Fahrenheit), anyone who succumbs to the elements might collapse and never recover, El-Katatney said.

"But regardless, people were still continuing to ... their ritual, where the stampede happened."

El-Katatney said she talked to some of the men who were caught in the mayhem.

"They told me how if you fell, if you weren't strong enough to withstand the pushing and shoving ... if you fell, you weren't going to get up again."

Inexperience and confusion

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Even though Saudi officials are extremely versed in hosting Hajj crowds, many of the pilgrims are making the journey for the first time and might not be prepared to follow all directions or handle the chaos.

"If any mistake happens -- if a group makes the wrong turn -- that will cause a disaster," Jamal Khashoggi of Saudi Arabia's El Arab TV told CNN. "And that's exactly what happened."

Maj. Gen. Mansour Al-Turki, the Saudi Interior Ministry's security spokesman, hinted that the problem may have stemmed from some pilgrims not following established guidelines, the Saudi Press Agency reported.

And novice pilgrims might try to "go on their own, or try to take a shortcut," Khashoggi said.

A deadly history

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Hundreds of other pilgrims have been killed during the same ceremony in years past. But Thursday's disaster was the deadliest at Mina since 1990, when 1,426 people died.

After a stampede during Hajj killed 363 people in 2006, the Saudi government erected three massive pillars and completed a $1.2 billion, five-story bridge near the site where pilgrims can toss stones.

But after the latest mass tragedy, many are wondering what more can be done to prevent it from happening again.