At least 717 pilgrims from around the world were killed in a stampede outside the Muslim holy city of Mecca in the worst disaster to strike the annual Hajj pilgrimage for 25 years.
At least 863 others were injured.
Saudi King Salman said he had ordered a review of hajj plans after the disaster, in which two large groups of pilgrims arrived together at a crossroads in Mina, a few kilometres east of Mecca, on their way to performing the "stoning of the devil" ritual at Jamarat.
It was the worst incident to occur at the pilgrimage since July 1990, when 1,426 pilgrims suffocated in a tunnel near Mecca.
Both incidents occurred on Eid al-Adha (Feast of the Sacrifice), Islam's most important feast and the day of the stoning ritual.
The Hajj, the world's largest annual gathering of people, has been the scene of numerous deadly stampedes, fires and riots in the past.
However, their frequency has been greatly reduced in recent years as the government spent billions of dollars upgrading and expanding infrastructure and crowd control technology.
Iran's Supreme Leader, Ayatollah Ali Khamenei, said the Saudi government should accept responsibility for the crush, in which more than 100 Iranian nationals were reported to have died.
King Salman offered deep condolences.
"We have instructed concerned authorities to review the operations plan ... (and) to raise the level of organisation and management to ensure that the guests of God perform their rituals in comfort and ease," the monarch said.
An Interior Ministry spokesman said the investigation would look into what caused an unusual mass of pilgrims to congregate at the location of the disaster. "The reason for that is not known yet," he told a news conference in Mina.
UN Secretary General Ban Ki-moon and the White House offered condolences.
"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," White House spokesman Ned Price said.
Iran's Tasnim and Fars news agencies reported that 125 Iranians were among the dead. Fars reported that Tehran summoned the Saudi charge d'affaires to lodge an official complaint over the disaster.
South African Acting President Cyril Ramaphosa extended condolences to families of the victims and said his government was awaiting information about his country's pilgrims.
The Department of Foreign Affairs has said it has received no requests for consular assistance in relation to the tragedy in Mecca.
A spokesperson said the Irish embassy to Saudi Arabia is continuing to monitor the situation.
Street 204, where the crush occurred, is one of two main arteries leading through the camp at Mina to Jamarat, the site where pilgrims ritually stone the devil by hurling pebbles at three large pillars.
In 2006, at least 346 pilgrims died in a stampede at Jamarat.
"Work is under way to separate large groups of people and direct pilgrims to alternative routes," the Saudi Civil Defence said on its Twitter account.
It said more than 220 ambulances and 4,000 rescue workers had been sent in to help the injured. Some of the wounded were evacuated by helicopters.
People continued with their pilgrimage despite the tragedy.
Two weeks ago 110 people died in Mecca's Grand Mosque when a crane working on an expansion project collapsed during a storm and toppled off the roof into the main courtyard, crushing pilgrims underneath.reported.
Saudi Arabia's health minister blamed "undisciplined pilgrims" for the stampede saying the tragedy would not have occurred if they "had followed instructions".
Health Minister Khaled al-Falih was quoted by El-Ekhbariya television as saying "many pilgrims move without respecting the timetables" established by authorities, which was the "principal reason for this type of accident."
"If the pilgrims had followed instructions, this type of accident could have been avoided."
Timeline of previous disasters during the Hajj pilgrimage
2006
6 January: 76 people die when a hotel collapses in the city centre.
12 January: 364 pilgrims killed in a stampede during the Mina stoning ritual in which hajj participants throw pebbles at three headstones, symbolising their rejection of Satan.
2005
22 January: Three pilgrims crushed to death in a stampede at the stoning ceremony.
2004
1 February: 251 people killed in a stampede at Mina, also at the stoning of the devil.
2003
11 February: 14 pilgrims, including six women, die on the first day of the stoning ritual.
2001
5 March: 35 pilgrims die at the ritual in Mina.
1998
9 April: More than 118 people killed and 180 injured in a stampede at Mina.
1997
15 April: A fire caused by a gas stove rips through a camp housing pilgrims at Mina, killing 343 and injuring around 1,500.
1995
7 May: Three people die and 99 are injured in a fire at the Mina camp.
1994
24 May: 270 people killed in a stampede during the stoning, an incident authorities attribute to "record numbers" of pilgrims.
1990
2 July: A huge stampede in a tunnel at Mina after a ventilation system failure kills 1,426 pilgrims, mainly from Asia.
1989
10 July: A twin attack on the outside of the Grand Mosque kills one and wounds 16. Sixteen Kuwaiti Shia are found guilty and executed weeks later.
1987
31 July: Saudi security forces suppress an unauthorised protest by Iranian pilgrims. More than 400 people including 275 Iranians are killed, according to an official toll.
1979
20 November: Hundreds of gunmen opposed to the Saudi government barricade themselves inside the Grand Mosque, taking dozens of pilgrims hostage. The official toll of the assault and subsequent fighting is 153 dead and 560 wounded.
1975
December: A huge fire started by a gas canister exploding in a pilgrim camp close to Mecca kills 200 people.
