Crown Prince Mohammed bin Nayef "was reassured of the progress of the ongoing investigation", the Saudi Press Agency said, in a rare update after he met on Sunday night with the investigative committee.
"He directed the members of the committee to continue the efforts exerted to come to the reasons behind the accident," SPA said.
Mohammed is interior minister and chairs the Saudi Hajj committee.
Saudi Arabia will remain in charge of Hajj, says prince
He ordered the probe immediately after the September 24 disaster during a stoning ritual at Mina, just outside the holy city of Makkah.
Saudi Arabia issued a death toll of 769 two days after the incident but has given no further tally or details of the casualties.
Data from foreign officials in more than 30 countries produced the toll of 1,791.
Pilgrims blamed the stampede on police road closures and poor management of the flow of hundreds of thousands of pilgrims in searing temperatures.
Saudi prince’s convoy triggered Hajj stampede: report
Saudi officials, speaking immediately after the disaster, blamed pilgrims themselves for not following rules.
The results of the probe will be presented to King Salman, who carries the title "Custodian of the Two Holy Mosques" in Mecca and Medina.
Salman has already ordered "a revision" of how the Hajj is organised.
Saudi Arabia's handling of the Hajj and its response to the disaster provoked foreign criticism, particularly from regional rival Iran, which reported the largest number of dead at 464.
At least 717 pilgrims killed, 863 injured in Hajj stampede at Mina
The hajj and lesser Umrah pilgrimages bring millions of Muslims to Saudi Arabia every year.
Salman said last week that the kingdom used "all its capabilities and efforts" to ensure the comfort and safety of pilgrims.
Days before the start of this year's Hajj at least 109 people, including foreign pilgrims, died in a separate accident when a construction crane collapsed on Makkah's Grand Mosque.
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