Officials from the United States, Turkey, NATO and the United Nations expressed condolences over the horrendous loss of life.
But Iran led the criticism of the Saudis, with Ayatollah Ali Khamenei blasting the Saudi government, saying it should accept responsibility for the disaster.
"Mismanagement and improper measures that caused this tragedy should not be overlooked," Khamenei said. "The Saudi government is required to accept its heavy responsibility for this bitter incident and meet its obligations in compliance with the rule of righteousness and fairness."
On Thursday, a deadly crush killed 717 people
as two lines of people converged during the Hajj, causing the annual pilgrimage's worst accident in 25 years.
For many, the trip of a lifetime
More than 2 million Muslims from around the world are in Saudi Arabia for the Hajj, a pilgrimage that all Muslims who have the financial and physical ability must make at some point in their lives. Many have saved for decades to make the journey.
Iran's semiofficial FARS News Agency said 131 Iranians were killed in the crush and 150 injured.
Other international officials were more charitable than the Iranians.
Speaking Thursday during an evening prayer service at St. Patrick's Cathedral in New York, Pope Francis said he wanted to express "my sentiments of closeness in the face of the tragedy that their people suffered today in Mecca."
"In this moment of prayer, I unite myself with you all in prayer to God, our father, all powerful and merciful," the Pope said.
U.N. Secretary-General Ban Ki-moon "was deeply saddened to learn of the death of more than 700 Hajj pilgrims and of injuries to many others as a result of the deadly incident," according to a U.N. statement.
Ban "extends his sincere condolences to the families of the victims and expresses his sympathies to all the governments concerned."
NATO Secretary General Jens Stoltenberg likewise offered his condolences.
"I am saddened by the death of hundreds of people in a stampede near the Muslim holy city of Mecca," Stoltenberg said. "The fact that this incident occurred during celebrations of Eid al-Adha makes it even more tragic."
Condolences to pilgrims' families
The White House also reacted with sorrow to Thursday's tragedy.
"The United States expresses its deepest condolences to the families of the hundreds of Hajj pilgrims killed and hundreds more injured in the heartbreaking stampede in Mina, kingdom of Saudi Arabia," National Security Council spokesman Ned Price said.
"As Muslims around the world continue to celebrate Eid al-Adha, we join you in mourning the tragic loss of these faithful pilgrims."
And Turkish President Recep Tayyip Erdogan, for his part, expressed condolences to the families of slain pilgrims, according to a statement issued by the Turkish presidency.
"I ask Allah to show mercy on all the Muslim brothers and sisters killed in the accident," Erdogan said.