Security forces intervened within minutes of the stampede starting to clear the bottleneck, ministry spokesman Maj. Gen. Mansour al-Turki told a press conference explaining how Thursday's deaths occured.
"Security forces were alerted to the incident immediately once it was seen through observation cameras, and moved in within two minutes," he said.
Out of 383 known dead, 203 have been identified, among them 118 men, 85 women, he said. Some 289 people were injured, but al-Turki said all but 45 have been released from the hospital.
Hundreds of worried pilgrims crowded around a photo display at a medical center on Friday, scanning anxiously for pictures of loved ones who may have been among the people killed.
The medical center on Friday posted photos of the unidentified dead. Egyptian Osama el-Gindy said he was looking for a relative who was a few meters ahead of him when the stampede began.
"I was slightly wounded but managed to pull myself out of the crowd. I haven't seen him since then," el-Gindy said. "I hope he is still alive. But if he is dead, he is a martyr and will go to heaven like all others."
Muslims believe that anyone who dies during a pilgrimage is assured a place in heaven.
Thursday's tragedy underlined the difficulty in managing one of the biggest religious events in the world, which this year drew more than 2.5 million pilgrims. The weeklong pilgrimage, required once in a lifetime of every able-bodied Muslim, ends Friday.
In the stoning ritual, all the pilgrims must pass by a series of three pillars called al-Jamarat, which represent the devil and which the faithful pelt with stones to purge themselves of sin.
The site, in a desert plain of Mina outside Mecca, has seen deadly incidents in seven of the past 17 years, including a stampede in 1990 that killed 1,426 people and another in February 2004 that killed 244.
Thursday's stampede began when some of the thousands who were rushing to complete the stoning tripped over baggage and caused a large pileup. Many pilgrims carry their personal belongings, such as tents, clothes or bags of food, with them as they move between the various stages of the hajj.
"It just started with a group of people pushing their way in and then finally they just got trapped and people started to step on bodies under their feet," one pilgrim told CBS Radio News.
The deaths follow another accident that marred this year's hajj, the Jan. 5being used as a pilgrims' hotel that killed 76 people in Mecca.
Ensuring a smooth pilgrimage is a key concern for Saudi Arabia's royal family, which bolsters its legitimacy by touting its role as the "custodian of the holy cities," Mecca and Medina, where Islam's 7th century prophet Muhammad was born and lived.
Crown Prince Sultan Bin Abdel Aziz said Thursday that the state had "spared no effort" to avoid such disasters but, he added, "it cannot stop what God has preordained. It is impossible."
"We feel pain and sorrow for them and for their families and we send our condolences," the prince said on Al-Ekhbariya television.
Saudi Arabia has made efforts to ease the massive flow of pilgrims since the 2004 stampede, widening ramps leading to the platform where the three pillars are located and creating more emergency exits.
The small, round pillars were replaced with 85-foot-long walls to allow more people to stone them at once without jostling each other. The walls extend down through the bridge and protrude underneath, so pilgrims below can also carry out the stoning without going above.
Thursday's stampede occurred below the platform, near one of the entrance ramps.
Many pilgrims expressed frustration over the repeated disasters at al-Jamarat.
"This should not happen every year. It should be stopped, it's a scandal. There must be a way to organize this better." Anwar Sadiqi, a Pakistani pilgrim, said.
Saudi Arabia has announced plans for further changes to the site in coming years that it says would allow some 500,000 pilgrims an hour to carry out the stoning.
Among the changes, the platform is to be expanded to four levels, with 12 entrances and 12 exits. Also, there are plans to bus pilgrims to al-Jamarat from a nearby tent city in the desert rather than allowing them to make their own way to the site.