Saudi Arabia’s most senior cleric, the grand mufti, has said the stampede at the annual Muslim pilgrimage to Mecca on Thursday was beyond human control.
He told the interior minister, Crown Prince Mohammed bin Nayef, that he was not to blame for the tragedy.
Iran and several other countries have criticised Saudi authorities for the way they handled safety issues.
Authorities have raised the number of deaths to 769 – the deadliest incident to occur during the Hajj in 25 years.
King Salman has ordered a safety review into the disaster, which injured 934 people, new casualty figures suggest.
The pilgrimage, or Hajj, is now into its final day, with no further serious incidents reported.
Analysis: Sebastian Usher, BBC Middle East editor
As criticism of the Saudis intensifies, so has the Saudi response. The intervention of the country’s top religious leader is no surprise. Nor is the grand mufti’s assertion that fate and destiny are inevitable.
Such fatalism has resonance in the Islamic world, but it won’t still a growing clamour of criticism.
Some of those who’ve been attending Hajj, including survivors of the crush, have been expressing a sense that the Saudis – despite all the billions they’ve spent on improving the Hajj infrastructure – have not done enough to ensure the safety of the majority of the pilgrims on the ground.
This has been magnified on social media, where the Saudi authorities’ placing of the blame on the pilgrims themselves for not following safety instructions has been seen by some as evidence of a lack of sensitivity towards those who come to the Hajj from poorer countries.
Why do millions gather in Mecca every year?
Grand Mufti Sheikh Abdul Aziz bin-Abdullah al-Sheikh was visited by the crown prince, who is also deputy prime minister and chairman of the Supreme Hajj Committee, on Friday evening, the official Saudi Press Agency (SPA) reported.
“You are not responsible for what happened,” the grand mufti said.
“As for the things that humans cannot control, you are not blamed for them. Fate and destiny are inevitable.”
The cleric’s remarks came after Iran’s Supreme National Security Council accused the Saudis of “incompetence” and urged them to “take responsibility” for the deaths.
And on Saturday, Prosecutor General Sayed Ibrahim Raisi said that Iran would seek the trial of the Saudi royal family over its “crimes” in “international courts”, Isna news agency reported.
Iran has so far reported the greatest number of deaths among foreign nationals, at least 134, with more than 340 of its citizens still missing.
A former ambassador to Lebanon is among the missing, state TV said.
The crush occurred on Thursday morning as two million pilgrims were taking part in the Hajj’s last major rite.
The pilgrims throw seven stones at pillars called Jamarat, which stand at the place where Satan is believed to have tempted the Prophet Abraham.
With temperatures around 46C, two massive lines of pilgrims converged on each other at right angles at an intersection close to the five-storey Jamarat Bridge in Mina, a large valley about 5km (3 miles) from Mecca.
It is also the second disaster to strike in two weeks, after a crane collapsed at the Grand Mosque in Mecca, killing 109 people.
Map showing location of Hajj crush – 24 September 2015
Deaths reported so far by nationality
Iran: at least 134
Morocco: 87 (media reports)
Cameroon: at least 20
Niger: at least 19
Somalia: 8 (media reports)
Other nationalities (numbers not yet known): Benin