King Salman, whose official title is "Custodian of the Two Holy Mosques" in Mecca and Medina, also ordered "a revision" of how the Hajj is organised.
On Saturday, groups of pilgrims were moving from early morning towards Jamarat Bridge for the last of three stoning days.
The interior ministry has said it assigned 100,000 police to secure the Hajj and manage crowds.
But pilgrims blamed the stampede on police road closures and poor management of the flow of hundreds of thousands of pilgrims in searing temperatures.
Abdullah al-Sheikh, chairman of the Shura Council, an appointed body which advises the government, stressed that pilgrims must stick to "the rules and regulations taken by the security personnel... In doing so, they protect their lives, their security and facilitate their performing of the rituals."
Health Minister Khaled al-Falih earlier made similar remarks that faulted the worshippers.
'Biased campaigns'
In comments carried late Friday by SPA, the Shura chairman called on citizens and Muslims to ignore "the biased campaigns carried out by the enemies of this pure country, to question the great efforts exerted by the kingdom to serve the holy sites, their construction and expansion, and to serve the visitors and pilgrims."
Riyadh's regional rival Iran said 131 of its nationals were among the victims, and on Friday stepped up its criticism of the kingdom, demanding that affected countries have a role in the Saudi investigation into the disaster.
"Saudi Arabia is incapable of organising the pilgrimage," said Ayatollah Mohammad Emami Kashani, leading the main weekly prayers in Tehran.
"The running of the Hajj must be handed over to Islamic states," he said.
Several African countries confirmed deaths in the stampede, as did India, Indonesia, Pakistan and the Netherlands. Moroccan media gave 87 nationals killed.
Nigeria's President Muhammadu Buhari urged King Salman "to ensure a comprehensive and thorough exercise that will identify any flaws in Hajj organisation".
Buhari said his country had lost a prominent journalist, a professor "and others" in the tragedy.
Largely incident-free for nine years after safety improvements, this year's Hajj was afflicted by double tragedy.
Days before it started, a construction crane collapsed at the Grand Mosque, Islam's holiest site, killing 109 people including many foreigners.
The Hajj is one of the five pillars of Islam, which each of the world's more than 1.5 billion Muslims is expected to perform.