Iran has led growing criticism of Saudi Arabia after at least 717 people died and 863 were injured in a stampede near the holy city of Mecca.
Iran's Supreme National Security Council accused the Saudis of "incompetence" and urged them to "take responsibility" for the deaths.
Nigeria has dismissed remarks by the Saudi health minister blaming pilgrims for "not following instructions".
King Salman has ordered a safety review for the Hajj pilgrimage.
The crush occurred on Thursday (local time) 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 from Mecca.
This is the deadliest incident to occur during the pilgrimage in 25 years.
It is also the second disaster to strike in two weeks, after a crane collapsed at the Grand Mosque in Mecca, killing 109 people.
Iran, Saudi Arabia's regional rival, has reported the greatest number of deaths among foreign nationals - 131 - and has reacted with the greatest anger.
On Friday, the spokesman for its Supreme National Security Council, Keyvan Khosravi, told the Isna news agency: "The unavoidable fact is that the Saudi government has been incompetent in this regard and with regard to the management of the Hajj pilgrimage, and Riyadh must accept responsibility for this."
He was echoing Supreme Leader Ayatollah Ali Khamenei, who said on Thursday that Saudi "mismanagement and improper actions have caused this catastrophe".
Iran has declared three days of national mourning. Protesters marched in Tehran shouting slogans against Saudi Arabia's ruling al-Saud family.
Alaeddin Boroujerdi, head of an Iranian parliamentary committee for national security, called on other Islamic countries to lodge protests with the Saudis.
The incident may worsen relations between the two countries, already strained by opposing stances on the conflicts in Syria and Yemen.