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.