Another 863 people were injured in the incident at Mina, which occurred as two million pilgrims were taking part in the Hajj's last major rite.
It is the deadliest incident to occur during the pilgrimage in 25 years. King Salman has ordered an urgent review of this year's Hajj plans "to improve the level of organisation".
The supreme leader of Iran, which lost at least 95 of its citizens in the crush, has criticised Saudi Arabia's preparedness.
It is the second disaster to strike Mecca in two weeks, after a crane collapsed at the Grand Mosque, killing 109 people.
Saudi Arabia's crown prince, Prince Mohamed bin Nayef, ordered a probe into how the tragedy had occured.
Nayef, who chairs the Saudi hajj committee, ordered the probe during a meeting with senior officials responsible for the pilgrimage in Mina, where the stampede took place.
The findings of the investigation will be submitted to King Salman, "who will take appropriate measures" in response, the Saudi Press agency said.
Mina is where pilgrims carry out a symbolic stoning of the devil by throwing pebbles against three stone walls. It also houses more than 160,000 tents where pilgrims spend the night during the pilgrimage.
Al Jazeera's Basma Atassi, reporting from Mina, said the incident took place in a street between pilgrim camps.
"The street where it happened is named Street 204. This stampede did not happen at the site of the 'stoning of the devil' ritual, which was happening today.
"During and after the stampede the pilgrims continued to flock into Mina to perform the devil stoning ritual."
Amateur video shared on social media showed a horrific scene, with scores of bodies - the men dressed in the simple terry cloth garments worn during Hajj - lying alongside crushed wheelchairs and water bottles.
The head of the Central Hajj Committee, Prince Khaled al-Faisal, blamed the stampede on "some pilgrims from African nationalities," Saudi-owned al-Arabiya TV channel reported.